Needing a win to boost its faint chances of reeling in the two Manchester clubs and Tottenham, fourth-place Chelsea was frustrated by poor finishing at Carrow Road, with misfiring Spain striker Fernando Torres being the biggest culprit.
Qualifying for the Champions League may be Chelsea's main target now, so news of Liverpool's 3-1 defeat at Bolton and Newcastle's 5-2 loss at Fulham will have been welcome.
Sixth-place Newcastle imploded after going into halftime 1-0 ahead, with United States attacking midfielder Clint Dempsey's second hat trick in three games helping Martin Jol's side to an amazing comeback win.
Liverpool was then surprisingly overrun by a Bolton team that had been languishing in the bottom three, surrendering an opportunity to move within three points of Chelsea.
League leader Manchester City hosts third-place Tottenham and Manchester United, which is second, visits Arsenal on Sunday in an important day for the title chasers.
At the other end of the standings, bottom team Wigan's plight worsened by losing 3-1 at Queens Park Rangers — its 13th defeat in 22 games.
Ireland striker Robbie Keane grabbed a second-half double — his second in the 84th minute proving to be the winner — as Aston Villa rallied to beat Wolverhampton Wanderers 3-2.
Keane was making his starting debut after moving to Villa on a short-term loan deal from Los Angeles Galaxy.
Sunderland beat Swansea 2-0, Blackburn grabbed a 1-1 draw at Everton and West Bromwich Albion claimed a first win in 2012 by beating Stoke 2-1.
Chelsea is now provisionally 10 points behind City and five adrift of Tottenham, but the margin should be shorter following a dominant second-half performance at Carrow Road that had Norwich hanging on.
However, Torres extended his goal drought to 15 club matches — the longest of his club career — by slicing wide a great chance in the 60th while Spain teammate Juan Mata also wasted a number of good opportunities.
"Because we want to be champions, it puts in things in a different perspective ahead of tomorrow's fixtures," Chelsea manager Andre Villas-Boas said.
"The games tomorrow can punish us hard in terms of what we were expecting. This could have been a good last opportunity for us to threaten for the title. The leaders can build a good margin."
Midtable Norwich's first clean sheet of the season in any competition was well-earned, leaving the promoted team ninth.
"The whole group put their bodies on the line when they had to, and it was a huge point for us." Norwich manager Paul Lambert said.
Danny Guthrie gave Newcastle the lead at Craven Cottage but Danny Murphy's penalty started Fulham's revival before Dempsey struck three times in a 30-minute span to take the United States attacking midfielder's tally for the London club to 52 in total, and nine in the league this season.
"Luckily the ball kept going in," said Dempsey, who became the first American to score a hat trick in the Premier League. "We never took our foot off the gas and we took our chances."
Bobby Zamora grabbed the hosts' fourth from the penalty spot, with the result lifting them well clear of relegation trouble and into 12th.
Liverpool has now just won one of its last six games and is sorely missing the presence of influential striker Luis Suarez, who is currently serving an eight-match ban for racially abusing Manchester United defender Patrice Evra.
To add to Liverpool's misery in a sluggish display at the Reebok Stadium, David Ngog — the striker it sold to Bolton in the summer — had a hand in the hosts' first two goals scored by Mark Davies and Nigel Reo-Coker.
Craig Bellamy reduced the deficit for Liverpool in the 37th but defender Gretar Steinsson scored Bolton's third goal, five minutes into the second half.
QPR moved out of the relegation zone with a second crucial victory in a week, coming four days after a 1-0 win over MK Dons in the FA Cup that kickstarted Mark Hughes' tenure as manager.
Heidar Helguson, Akos Buzsaky and Tommy Smith were the goalscorers for QPR, with Colombia striker Hugo Rodallega replying for Wigan.
Australia midfielder Tim Cahill went from hero to villain for Everton, opening the scoring against Blackburn with his first goal in 13 months but then seeing his goalline clearance strike visiting forward David Goodwillie in the chest and rebound into the net for the equalizer.
Stephane Sessegnon and Craig Gardner scored for Sunderland as the team's revival under new manager Martin O'Neill continued.
Graham Dorrans' was the matchwinner for West Brom at Stoke, his injury-time free kick through a crowd of players bringing the team a first league win since Dec. 21.