Goals from Milan Baros, Djibril Cissé and a deflected effort from Luis Garcia's, which struck Craig Fleming, were more than enough to see off the East Anglians, who were disappointing.
The home team's defence allowed Norwich nothing and Jerzy Dudek in the home goal did not have a shot to save throughout the entire game.
Gerrard's usual berth in midfield was filled by Dietmar Hamann, making his 150th appearance for the club. The England midfielder's metatarsal fracture is likely to keep him out of contention for up to eight weeks, so the German looks set for a prolonged spell in the team.
Harry Kewell was absent, too, and his place went to the promising Stephen Warnock who has impressed in recent appearances from the substitutes' bench.
For Norwich's director Delia Smith it was a first visit to Anfield and she was hoping the East Anglians could end a dismal run of six Premiership games without a win. That said, they have battled well against Manchester United, Newcastle, Arsenal and Spurs.
Both sides showed aggressive intent from the start and Liverpool gave Robert Green an early scare when Garcia cut in from the right and struck a rising shot that flew narrowly wide of the keeper's far post.
Warnock kept up the pressure with a first-time cross that reached Garcia. His header caused panic in the defence and when Green slipped on the heavily watered pitch, Cissé missed a good chance by heading over the bar with the goal unguarded.
Then Norwich found their touch, if only briefly, as Darren Huckerby drifted past three defenders but unluckily ran the ball out of play.
Hamann was playing a much deeper role than is normally occupied by Gerrard. His natural tendency is to defend and Liverpool missed the England dynamo's forward promptings.
Green, who is on Sven-Göran Eriksson's list of potential goalkeepers, looked far from international class when he spilled a routine cross and was grateful to see Simon Charlton hack the ball to safety.
Baros was playing to form: covering yards of pitch and harrying the Canaries defence. One clever pass to Cissé may have brought a goal had it not been for quick thinking by Fleming.
Then, in the 23rd minute, Baros gave Liverpool the lead with a tremendous shot from the edge of the area, one that flew past Green. It was very much a solo effort: the Czech made himself an opening by drifting away from two defenders and the finish, with his right foot, was spectacular.
Three minutes later, Liverpool were 2-0 up. Cissé sliced open the visiting defence with a ball that Garcia hit on the turn. His shot may well have been goal-bound but it struck Fleming on the back and flew past Green, who was wrong footed. Not surprisingly, the Norwich players looked stunned and it was left to Huckerby to show the signs of spirit.
Liverpool kept up the pressure and twice Baros had Green diving across his goal to keep out testing shots.
No doubt disappointed with his team's lack of attacking threat, Norwich's manager Nigel Worthington brought on David Bentley and Leon McKenzie for the second half. But, prompted by the quicksilver Garcia, Liverpool kept up the pressure and Green was called on to keep out shots from Cissé and Baros.
Liverpool's third came in the 64th minute, following a well-worked free-kick. John Arne Riise touched the ball to Xabi Alonso who, in turn, rolled it into the path of Cissé and his low shot found the corner of the net with Green unprotected by his defensive wall.