The Canaries climb to the 12th place in the Premier League after a late winner from their captain leaves David Moyes' side six points off a top-four spot following Arsenal's winKei Kamara and Grant Holt completed a late comeback for Norwich against Everton to pick up an important three points at Carrow Road, after Leon Osman had given the Toffees the lead in the first half.
Kamara's header and Holt's tap-in proved to be too much for Everton to handle, despite a resistant defence keeping the Canaries out until the late stages of the game.
A defeat for David Moyes' side leaves them six points off of fourth spot, and even though Norwich have won only once in their last 10 fixtures, Chris Hughton's side climbed to 12th place.
Luciano Becchio and Holt started up front for the hosts, with Wes Hoolahan moving to the left wing, while Jonny Howson came into the starting lineup for Alex Tettey.
Kevin Mirallas was replaced in the starting lineup by Steven Naismith, while Victor Anichebe missed out through injury and Seamus Coleman returned after missing the last five games.
Robert Snodgrass was denied the first clear chance of the game, when his shot from six yards out was deflected over the bar by Sylvain Distin. Everton hit back immediately though, with Jelavic forcing Mark Bunn to parry the ball to safety early on.
A great piece of build-up play by Everton saw Jelavic chest down the ball to the feet of Marouane Fellaini, but Michael Turner brilliantly blocked the attacker’s shot on the edge of the penalty area.
And in the 39th minute later Osman broke the deadlock as he found space in the six yard-box to head in Baines' cross after some great build-up play from Pienaar and Fellaini, all resulting from a free-kick near the half-way line.
Everton came out the stronger side in the second half with Baines and Fellaini testing the Norwich defence in the early moments of the second half, although a lack of precise passing in the final third of the pitch provided no clear chances for the away side.
Holt joined Baines in the book after the striker was deemed to foul Coleman near the half-way line, although the Toffees did little with the resulting free-kick.
Kamara came onto the field just before the 60th minute for Becchio, and made an impact almost immediately, setting himself up with a scissor-kick volley which Howard pushed away.
Some good deliveries by substitute Anthony Pilkington and Snodgrass gave the home side some hope in the closing stages of the game, but Howard was repeatedly quick off his line to prevent any clear-cut chances for Norwich.
Norwich finally got an equaliser in the 84th minute though Kamara, who got his first Premier League goal for Norwich by nodding in Snodgrass' corner.
The Canaries were close to grabbing a winner in the 91st minute, before what looked to have been a game-saving challenge from Distin.
But, with stoppage time almost over, Norwich captain Holt tapped the ball into an empty with Howard off of his line following Martin's cross into the Everton penalty box to seal the win for the hosts.