At the other end of the table, bottom club West Bromwich Albion drew 0-0 with Newcastle United, Crystal Palace climbed out of the relegation zone with a 2-0 win over Aston Villa, and Blackburn Rovers beat Charlton Athletic 1-0.
Goals from Spanish forward Luis Garcia and Norwegian midfielder John Arne Riise within five minutes in the second half of a lacklustre match sealed Liverpool's victory at Norwich.
The Merseysiders moved to 37 points, two ahead of Middlesbrough, who play at league leaders Chelsea on Tuesday.
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 doubled the advantage in the 63rd minute when a clearance cannoned back off Liverpool substitute Florent Sinama-Pongolle.
His shot was parried by Green, only for the ball to fall to the unmarked Riise who calmly slotted into the empty net.
Ryan Jarvis caused Liverpool late anxiety when he curled a left-foot shot into the top corner of Jerzy Dudek's goal in the dying minutes but the visitors held on to leave Norwich 18th in the standings.
Striker Andy Johnson was Crystal Palace's
Johnson opened the scoring in the 33rd minute, latching on to a rebound after Ben Watson's long shot was blocked by keeper Thomas Sorensen, and the prolific forward converted a penalty after 66 minutes to leave Villa ninth in the table.
Blackburn midfielder Brett Emerton headed in David Thompson's 41st-minute cross to secure victory for Mark Hughes's struggling team against Charlton. Rovers climbed a place to 15th, while Charlton remained eighth.
Newcastle overcame severe injury problems to dominate the match but were unable to break down a stubborn West Brom side who earned their first home point under new manager Bryan Robson.
Newcastle midfielder Lee Bowyer came closest to scoring when his rasping 20-metre drive came back off a post midway through the first half but Graeme Souness's team's frustrating season continued as they remained 13th.
West Brom remained rooted to the bottom but closed the gap on Southampton to a point.
On Tuesday, second-placed Arsenal host Manchester City, Manchester United entertain Tottenham Hotspur, Portsmouth visit Everton and Birmingham City face Bolton Wanderers.
Southampton and Fulham complete the 22nd round of Premier League matches on Wednesday.
