The fourth seed, who is regarded to have an extremely tough draw, had little trouble dismantling his opponent’s game in a brilliantly savage display.
Davydenko saw the first two sets slip by, only managing to muster a meagre two games in response, and a slight improvement in the third was not sufficient as Murray romped to a comprehensive victory.
It was an utterly convincing win for the British number one, who never afforded his opponent a glimmer of an opportunity to get a foothold in a match he dominated from start to finish.
"I struck the ball well," Murray said. "I tried to use the slice to mix it up and it worked well.
"I played well and once I got ahead I wanted to make sure I didn't let him back in. I needed to stay concentrated on my serve and I did it well. It was such a convincing victory."
Murray pointed skywards in an animated victory celebration, perhaps relieved at coming through so easily after his preparations were hampered by early exits from warm-up tournaments and injury problems.
But he refused to explain why he did it.
"I don't want to say too much about it because otherwise I will be asked about it the whole tournament," he said. "I'm not going to give any more details about what it was."
Coming into the match Murray shaded the pair's head-to-head record 5-4, with their last encounter at the Montreal Masters back in 2009; but the disparity in class was vast on the grass.
The former world number three began sluggishly as Murray was able to stamp his authority on the match in the third game with a clinical break of serve.
It was a bright start from Murray as he held serve with consummate ease and relentlessly attacked his opponent’s delivery, breaking for a second successive game to establish a 4-1 lead.
Another break of serve left Davydenko looking very despondent as he won just a solitary game in the opening set, and the Russian was left floundering as his slump continued into the second.
Murray pounced ruthlessly to break his opponent’s serve once more in the second game of the second set, and he assumed complete control as he surged into a 4-1 lead once more.
The 31-year-old from Moscow could not haul himself back into the set as he saw the second go exactly the same way as the first in ignominious fashion.
The pressure from Murray on his opponent’s serve was incessant as Davydenko again buckled at the start of the third set.
A flurry of belligerent groundstrokes ensured that Murray seized control of the third set from the very first game, breaking Davydenko’s serve with alarming ease.
The Russian battled to restore parity, but Murray held firm on serve and was unerring on his first delivery, which restricted his opponent to speculative flashing returns.
The fourth seed closed out the third set for the loss of four games as he secured his progression in fine style, with the Centre Court crowd clearly enjoying a sparkling display from the Brit.
Murray will next take on either gigantic Croat Ivo Karlovic or Israel’s Dudi Sela in the second round.
World number two Rafael Nadal made a slow-burning start to his Wimbledon campaign, with the Spaniard caught cold by 80th-ranked Brazilian Thomaz Bellucci before coming through 7-6 6-2 6-3.
The French Open winner, champion at Roland Garros for a record seventh time this year, was 4-0 down in an hour-long first set as his timing went awry in a battle of left-handers under cloudy skies on Centre Court.
Any alarm was momentary with Nadal fighting back to 4-4 and winning the eventual tiebreak 7-0.
The press box benches that had filled halfway through the set emptied just as swiftly knowing that normal service had resumed.
The world number two, perhaps sensing the crowd were growing impatient for the Andy Murray show to follow immediately after, took just half an hour more to go two sets up and wrapped up proceedings in two hours 15 minutes.
"I think today I didn't play my best match," Nadal said with some understatement. "I think especially at the first set I played a little bit too nervous, a little bit not knowing exactly what to do.
"My movements were a little bit in a defensive way, not an aggressive way."
Serving to open the match, Bellucci fired two aces in the first game and then broke Nadal with a lucky net cord that stretched the Spaniard and left him defenceless against the stinging reply.
He held serve, with Nadal firing a return to the net at 40-30, and then chalked up another break when the Spaniard hit low again.
That was about as good as it got for the Brazilian against an opponent who has never lost a first round match in any grand slam tournament.
With cries of 'Vamos Rafa' echoing around the court, Nadal powered back with a sense of momentum.
With the crowd in no doubt about the outcome, the mood lightened.
"Come on Rafa, don't give up," some humourous soul shouted as the world number two was briefly pegged back by Bellucci to 30-30 at 5-3 in the third set.
"Come on, Andy," declared another more impatient voice to a ripple of appreciative laughter.
Bernard Tomic admitted he had been "slacking off" following his 3-6 6-3 6-4 6-4 defeat by wildcard David Goffin in the Wimbledon first round.
The Australian teenager enjoyed a shock run to the quarter-finals last year as an 18-year-old, but on his return to Wimbledon's lawns was overwhelmed by a fresh-faced Belgian opponent.
"To have talent is one thing, it's huge for any sport," 20th seed Tomic said.
"But I have sort of slacked off a little bit and look what it's costing me. Last eight, nine weeks I'm losing a lot of first, second rounds. So it's not my quality of tennis.
"My quality of tennis should be getting me to a lot of semi-finals, finals at tournaments or even winning, but lack of concentration, not working hard, it costs you."
Tomic played well enough in the first set but Goffin roared back, bringing his inspired Roland Garros form to the grass courts on his Wimbledon debut. The Belgian reached the fourth round in Paris as a lucky loser.
"Well, look, he's 21. I'm 18, 19. I've gotten into the top 30," said Tomic. "It's different. He has time and he's going to obviously be a top-30 player. He has great groundstrokes.
"But I think what I've lacked the last few weeks is the consistency and it's tough to get."
Tomic will get an early chance to return to Wimbledon when he plays in the Olympic Games which start next month.
"I'm really lucky for that opportunity to have the Olympics coming up, which is, from my point of view, bigger than Wimbledon," he said.
"For any athlete I think it's something that I want to do well in and I'm thankful it's on grass."
Former Wimbledon champion Lleyton Hewitt, reduced to being a wildcard at the tournament he won 10 years ago, could never match the firepower of number five seed Jo-Wilfried Tsonga who eased to a 6-3 6-4 6-4 victory in their first round match.
But the gritty Australian is certainly not ready to say goodbye to the place that means so much to him.
Coming off Number One court, he heard that he had also been given a wildcard to the Olympics at Wimbledon next month.
"At least I get to play here again. That is a bonus," he said.
Hewitt scuttles around the court like a feisty terrier, never giving up and chasing every ball to the ends of the court.
That doggedness brought him two grand slam victories, the 2001 US Open and Wimbledon the following year. It also armed him with the determination to battle against a string of injuries from groin problems to toe surgery.
"I'm proud of myself for what I have been able to do, all the hard work it's taken to get here," he said.
A 30-strong army of Hewitt fans, sporting green and yellow shirts and baseball caps in the colours of the Australian flag, chanted; "Let's Go Lleyton, Let's Go."
But their rousing cheers were never enough to raise the game of the diminutive Hewitt against the mighty Frenchman who is ranked sixth in the world and caused a major shock at Wimbledon last year when he beat Roger Federer after fighting back from two sets down.
Hewitt is 202nd in the world rankings and has won 105 matches on grass. Only Federer of active players, with 106, has more victories on the surface.
His devoted fans chorused "Walking along, singing a song, walking in a Hewitt wonderland."
It was in vain but at 31 years old Hewitt is in no hurry to head off into the sunset.
"I'd like to be back here next year," he said. "Absolutely.
"I'm an athlete. You never love losing. I'm still playing the game to compete, to be out there."