Goals from Spanish forward Luis Garcia and Norwegian midfielder John Arne Risse within five minutes of each other in the second half of a lacklustre match were enough for Liverpool to move to 37 points, two ahead of Middlesbrough, who play league leaders Chelsea on Tuesday.
Ryan Jarvis scored his first Premier League goal in the 88th minute for Norwich who remain on 16 points in 17th place, just one point ahead of Crystal Palace, who host Aston Villa later on Monday.
Garcia broke the deadlock in the 58th minute with a delicate first-time lob over Norwich goalkeeper Robert Green after a pinpoint 50-metre pass from Riise.
Riise then doubled the advantage in the 63rd minute when a clearance cannoned back off Liverpool substitute Florent Sinama-Pongolle who found himself free.
His shot was parried by Green, only for the ball to fall to an unmarked Risse who calmly slotted into the empty net.
Jarvis created some anxious final moments for Liverpool when he curled a left-foot shot into the top corner of Jerzy Dudek's goal in stoppage time.
