A Robert Snodgrass goal early in the second half consigned Tottenham to a 1-0 defeat on Sunday that left the London club six points off the top four, while Norwich moved four points clear of the relegation zone.
"I felt we deserved it, we could have taken more pressure off ourselves," Norwich manager Chris Hughton said. "We had other good opportunities and kept up our level of performance. I'm immensely proud of the team."
Snodgrass got past Danny Rose on the left of Tottenham's defense before drilling past Hugo Lloris in the 47th minute at Carrow Road. Bradley Johnson was then unlucky not to double the lead when his long-range free kick smashed against the underside of the crossbar. Nathan Redmond also brought a fine save from Lloris after working a shooting opportunity in the area.
Snodgrass said the importance of the win couldn't be overplayed.
"It's massive, especially with the teams about us losing," Snodgrass said. "I think the performances over the past 3-4 weeks have been terrific. We've been shooting ourselves in the foot with silly mistakes."
Substitute Roberto Soldado wasted a good chance for Tottenham, sending his shot wide after being set up by Emmanuel Adebayor.
Norwich goalkeeper John Ruddy did well to block an attempt from Adebayor as Spurs failed to break down the hosts' strong defense.
Liverpool beat Swansea 4-3 on Sunday to maintain its Premier League title challenge thanks to two goals each from Daniel Sturridge and Jordan Henderson.
The goals took Liverpool's tally in the Premier League this season to 70, overtaking Manchester City as the top scorers, and left the fourth-place team just four points behind league leader Chelsea.
However, manager Brendan Rodgers refused to be drawn on Liverpool's title hopes.
"I think for us, we're concentrating on our performance," Rodgers said. "We're just concentrating on winning games. No one is really talking about us for the title anyway. Everything now is about Chelsea, Manchester City and Arsenal."
Sturridge's first came in the third minute when he received a through ball from Raheem Sterling before rounding Swansea goalkeeper Michel Vorm and firing into an open goal. The striker then provided the assist for Henderson to double Liverpool's lead in the 20th from the edge of the area.
Jonjo Shelvey pulled one back for Swansea against his former club three minutes later with a long-range strike that went in off the crossbar. He held his arm up in apology to his former club, a gesture that received applause from the Liverpool fans.
But the home supporters were shocked into silence soon after when Wilfried Bony equalized in the 27th minute, with his header from Jonathan De Guzman's free kick taking a slight deflection off Martin Skrtel.
Sturridge gave Liverpool a 3-2 lead at halftime when he headed in from close range after a Luis Suarez cross had found him unmarked. Swansea levelled soon after the interval though when Bony scored a penalty after being fouled by Skrtel.
Suarez went close to restoring Liverpool's lead but Vorm saved well when one-on-one with the striker before De Guzman nearly gave Swansea the lead when he shot just wide from a free kick.
Henderson struck the winner after receiving a pass from Suarez. His initial shot was parried by Vorm but the England forward reacted quickest to poke the ball in from close range.
Despite the victory, Rodgers is hoping to see an improved defensive display against Southampton next weekend.
"At 2-0, we should manage the game better," Rodgers said. "We are obviously very disappointed with the goals we conceded."
Swansea manager Garry Monk tried to take the positives out of the defeat.
"I can't complain about the effort from my players," Monk said. "Going forward, I think it's a confidence boost to them that they can come to somewhere like this - where a lot of people thought they would wipe the floor with us, the way they've been dismantling teams here - and we were in the game right up until the final whistle."