The Uruguayan struck twice in the space of four minutes midway through the first half to put the Reds in command.
After Norwich - who are all but secure of a place in the Premier League heading into their final two games - rallied briefly, Suarez completed his treble eight minutes from time with an audacious lob from just inside the Norwich half to give Kenny Dalglish's men the perfect tonic ahead of their Wembley date with Champions League finalists Chelsea next Saturday.
Reds captain Steven Gerrard had been restored to the starting XI after being rested for last weekend's disappointing home defeat by West Brom which was a seventh in 10 Premier League games.
The Carrow Road pitch had been drenched for several hours this afternoon, making for testing conditions during the opening exchanges.
Norwich winger Anthony Pilkington slipped as he looked to cut back inside after getting clear down the left, before keeper John Ruddy was also on the floor at the edge of the penalty area as the ball squirmed loose.
On eight minutes, Norwich left-back Adam Drury pulled up with a groin injury and was eventually replaced by Russell Martin.
Despite Liverpool having the better of possession, Norwich fashioned the first real opening when Pilkington got away down the left again, and his low centre was hacked clear by Jamie Carragher with Steve Morison waiting at the back post.
Craig Bellamy - who came through the Norfolk club's youth team before being sold to Coventry for £6.5million in August 2000 - moved down the Norwich left and floated a cross into the area, but Stewart Downing lost his footing and somehow could only hack the ball back out of the box.
The visitors went in front on 24 minutes.
Gerrard battled to win the ball out on the left from David Fox, and fed Suarez, who took one touch on into the Norwich area before lashing home into the top-right corner.
It was almost 2-0 soon after when Suarez stretched the hosts again down the right and crossed for Gerrard, whose goalbound effort hit Ryan Bennett and flew behind, as the Reds appealed for what would have been a harsh handball against the defender.
Liverpool, though, did double their lead on 28 minutes.
Again Suarez was proving too much for the Norwich defence to handle, as this time he robbed Elliott Ward following a short pass out on the right and darted into the box, before this time drilling a low strike across Ruddy and into the bottom corner.
Liverpool's quick double salvo had silenced the home crowd and the visitors were now in cruise control heading into half-time.
Norwich made a change for the start of the second period as former Everton striker James Vaughan, back from a series of niggling injuries, replaced Fox.
It was a lively return by the home side, who forced a couple of corners.
Elliott Bennett forced Jose Reina into a full-stretch save with a fierce 20-yard strike, while Bradley Johnson glanced his header wide from the resulting corner.
Liverpool almost put the game beyond Norwich on 51 minutes when was played in down the right and his cross caused panic in the Norwich six-yard box before Jonjo Shelvey headed against the crossbar.
The former Charlton midfielder then somehow failed to make contact with a low ball across the face of goal from Jose Enrique.
Ruddy made another good stop to deny Downing as the England man cut in from the right and flashed in a low shot.
As the hour mark passed, it was all Liverpool.
Suarez was played through on goal in the 65th minute.
However, the Uruguay forward tried a cheeky chip from 12 yards, which floated over the keeper and cleared the crossbar - much to the amusement of the Norwich faithful behind the goal.
With 15 minutes left, Norwich sent on captain Grant Holt, who had scored in the 1-1 draw at Anfield earlier this season, as he replaced Morison.
Bradley Johnson let fly from 25 yards, but was well off target, which just about summed up the afternoon's display by the home side.
Suarez completed his hat-trick on 82 minutes as this time his stunning perfectly-weighted lob over Ruddy from just inside the Norwich half dropped into the net.