The number two seed was far from his best in the win over Germany's Becker but progressing with minimum fuss from the early rounds is key to a winning strategy in a fortnight long Grand Slam.
Murray's last appearance on the All England Club's hallowed centre court was exactly 323 days ago - when he scooped a famous Olympic gold with another straight sets win.
The world number two and US Open champion dropped just seven games in that remarkable win over Roger Federer but was given arguably a more thorough examination by big-serving Becker.
"It was a good match, he played some solid tennis and didn't give much away in the first two sets," said Murray.
"I started to play a bit better in the third set but it's a good start. He's a good grass court player but I was ready and to win in three sets is pleasing because there are always nerves in the first match, especially here."
Becker, the world number 92, had lost their only previous encounter, just two weeks ago at Queen's Club, but that match had stayed close throughout.
Murray broke early to establish an initial advantage but his rival won three games on the spin and saved a late set point before the home hope closed out the opener after an exchange of fizzing forehands.
But last year's beaten finalist was still struggling to find his normal rhythm, making an uncharacteristic number of unforced errors that, if repeated, will certainly be heavily punished by the tougher tasks that await.
However, he also was converting his fair of share winners and he secured the second set with ease and then established an early and ultimately decisive advantage in the third.
As errors crept into Becker's game, Murray took each chance to exert his authority booking his second round date with Taipei's Yen Hsun-Lu who beat fellow British player James Ward.
And there was more good news for Murray as his already tough route to a second consecutive final became just a little easier.
Murray could have faced two-time champion and number five seed Rafael Nadal in the latter stages but for the second straight year he suffered a shock early exit, although this was his first-ever opening round loss in a Grand Slam.
After his second round defeat to Lukas Rosol 12 months ago, the clearly out-of-sorts Spaniard lost 7-6, 7-6, 6-4 to world number 135, Belgium's Steve Darcis.
"That is sport and sometimes you lose," said Nadal. "Not a lot of things were good but Darcis played well and that's it.
"It was just not the right day for me, I tried my best but it wasn't possible for me."