Though Norwich defended poorly throughout, captain Elliott Ward having a particularly torrid afternoon, Suarez was sublime, his third coming via a long-range chip that soared over John Ruddy and nestled in the back of the net for one of the goals of the season.
Suarez had earlier reached double figures for the Premier League campaign with two stylish finishes in the first half, the first following a mistake from David Fox and the second following an error from Ward.
As preparation for next weekend's FA Cup final against Chelsea the victory was perfect for Liverpool, the performance being in stark contrast to the frustration that has dogged their league campaign and had grown alarmingly following a run of seven defeats in 10 games prior to the trip to Norwich.
The win takes Liverpool to within two points of seventh-placed Everton, while Norwich, who could have drawn level with Kenny Dalglish's side with a victory, drop down to 13th.
While Norwich surprisingly dropped Grant Holt from their starting XI, Andy Carroll was absent from Liverpool's matchday squad entirely due to a groin strain, though it is not thought to be serious ahead of the FA Cup final. With Carroll absent, Suarez was given the opportunity to play as the advanced forward and link up with Gerrard.
It was a combination that worked to great effect, and after an otherwise dismal start to the game at Carrow Road, the two Liverpool stars combined to give the visitors the lead after 24 minutes.
Gerrard exploited a moment of hesitancy from Fox as he closed the Norwich midfielder down quickly and robbed possession, playing a quick pass into Suarez who from just inside the box guided a fantastic shot past Ruddy and inside the far post.
Norwich's defending left plenty to be desired and within minutes they were exposed again. Suarez got a bit of luck when sneaking past the compromised Ward and after receiving a square pass Gerrard saw a firm effort deflected wide of the goal off the arm of Ryan Bennett. Liverpool's claims for a penalty were ignored.
However, after 28 minutes, Suarez did extend Liverpool's lead. Again Ward was culpable as he went in half-heartedly on Suarez on the right wing and the forward skipped away with ease, driving towards the box and dispatching a wonderful low effort that flew past Ruddy and nestled just inside the far post.
To complete a miserable first half for the Norwich captain, Ward was then booked for a foul on the lively Suarez, who tormented the home side at every opportunity when exhibiting the side of his game that helps to make him such a compelling player.
Norwich emerged from the break in much better shape, replacing Fox with a forward in James Vaughan to give them more presence in attack, and began to threaten the Liverpool goal with Elliott Bennett forcing Pepe Reina into a smart stop with a rifled effort from 20 yards.
However, Liverpool were still the more potent side and Jonjo Shelvey twice threatened to make it 3-0. The young midfielder first hit the bar with a header after a Suarez shot had deflected up and into his path, before then wasting a glorious chance when diverting the ball up into the air from close range when meeting a cross from Jose Enrique.
Stewart Downing joined in when seeing a low effort repelled by Ruddy and Suarez was then denied a hat-trick in agonising fashion. Ward failed to clear on the edge of the box and the forward then put the ball through the legs of Ryan Bennett before dinking the ball over Ruddy and just over the bar.
Popping up through the middle and in wide positions, Suarez was at his electric best and Norwich defender Ryan Bennett was booked after twice grabbing hold of the forward having run out of legal ways to inhibit his opponent.
Norwich's most lively attacker was the substitute Vaughan, and after hitting one shot just wide of the upright following a smart turn 20 yards from goal, he then directed a header narrowly wide when meeting a cross from the right from Russell Martin. Vaughan then saw a fantastic volley blocked by Carragher as the former Everton striker was left frustrated once again.
However, the last word was to go to Suarez on a fine evening for the Uruguay international. When Ward, again, failed to deal with the ball on the half-way line, Suarez pounced, taking two touches before spotting Ruddy off his line and floating the ball over the keeper from all of 55 yards.