Aston Villa clinched just their third league win of the season to pile the relegation pressure on Norwich too.
Joleon Lescott and Gabby Agbonlahor's first goal for 11 months sealed a 2-0 win, although Villa are still eight points from safety.
Remi Garde's side remain bottom of the Premier League but the Frenchman has at least given the strugglers fight.
The Canaries dropped into the relegation zone after Newcastle's 1-0 win against West Brom and Alex Neil's side are in serious trouble after six straight defeats in all competitions.
Villa are still likely to get relegated and, on this evidence, the Canaries will join them in the Championship next season.
Agbonlahor, leading the line with Jordan Ayew banned, gave Norwich an early warning when he stabbed wide after 10 minutes but the game struggled to ignite, despite the importance for both sides.
Norwich lacked the quality going forward and failed to keep possession well enough to threaten Villa.
Dieumerci Mbokani fired at Mark Bunn but it was a token effort during a poor first half which also saw Carles Gil fire a free kick widely over.
A turgid game was finally interrupted on the half hour when Sebastien Bassong wasted the Canaries' best effort.
The defender was left unmarked at the far post but could only head Russell Martin's cross into the ground and over.
In the context of the game it was a huge chance with both teams out of form and confidence but Villa grabbed a vital lead a minute before the break.
Mbokani needlessly brought down Micah Richards on the right and Lescott met Gil's free kick at the far post - after wrestling Mbokani away - with his header going in off Timm Klose.
It gave Villa belief and they got breathing space when Agbonlahor doubled their lead six minutes after the break.
The striker, whose last goal game in March 2015, beat the Norwich offside trap to Ashley Westwood's pass and - with Declan Rudd rashly rushing from goal - slid in from the edge of the box.
With the weight lifted, Villa relaxed and rarely looked like blowing their lead. Gary O'Neil poked Naismith's cross wide but pedestrian Norwich were easy pickings for Villa.
And with 20 minutes left Leandro Bacuna should have finished the game but blazed over with just Rudd to beat from eight yards.
It was a let off for demoralised Norwich and they tried to, finally, mount a recovery but first Jores Okore and then Gil cleared from Martin and Bassong with 10 minutes to go.
Villa were clearly nervous as the Canaries enjoyed possession at the end and almost grabbed a consolation with two minutes left.
Mbokani's drive hit Lescott and spun across goal only for the striker to be denied by a combination of Bunn and Richards as Villa held on.