French midfielder Lees-Melou's ninth-minute deflected shot, which went in off the post, put the hosts on their way before Pukki drilled home the second to give Norwich a glimmer of hope of staying up, with Dean Smith's side now seven points from safety with seven matches left.

Burnley had their moments, with Maxwel Cornet, the match-winning hero against Everton in midweek, missing a glorious chance from three yards out.

In what was a must-win game, Norwich's defence came under relentless pressure at times but recorded back-to-back clean sheets in the league for the first time since October.

"We know it's hard and still a mountain but we have seven games to go now, so if you put a few wins together the table looks different," said Norwich boss Smith.

We still believe we can stay up - Norwich boss Smith

The result leaves the Clarets 18th in the table, four points from safety with eight matches remaining.

"It's still the same challenge but a game down," Burnley manager Sean Dyche said.

Gritty Norwich show fight - but have they left it too late?

With struggling Everton beating Manchester United on Saturday, Norwich started Sunday's game 10 points from safety with eight matches left.

But Smith's side passed the pressure test in style with a first win in nine league games.

It will still require a monumental effort for them to survive. Three of their final seven matches include teams challenging for Europe - West Ham (home), Tottenham (home) and Manchester United (away).

"We want to take it to the last game, but we know how hard it could be," added Smith. "Hopefully we can find that resilience in the results."

Pukki's goal was his 20th in the Premier League, making him Norwich's third top scorer in the competition (behind Chris Sutton on 33 and Grant Holt on 23)

Even before Lees-Melou's goal, Milot Rashica forced Nick Pope into a diving save, while the Burnley keeper denied Pukki with his legs.

Just as impressive for Smith was his side's performance at the back.

Norwich made several vital blocks to frustrate Burnley, including one by former Clarets defender Ben Gibson to keep out Ashley Westwood's volley.

In the closing stages, Norwich's Grant Hanley headed against the bar while Pope denied Rashica before Pukki had home fans celebrating a rare win.

Burnley's survival hopes suffer major setback

Cornet will have nightmares about his 65th-minute miss, just days after he left the pitch at Turf Moor with fans singing his name following his late winner against Everton.

He looked certain to equalise as he slid to meet Dwight McNeil's lovely pass, but somehow put it wide as Burnley failed to score for the 15th time in the league this season.

"We can't miss chances like that," Dyche said. "He's done well for us this season. But we have to take the game on and be better than that in the front third."

Earlier, Cornet was denied by Tim Krul, but the Norwich keeper was not tested nearly enough in what was a high-stakes game.

Burnley have won just four Premier League matches all season

Dyche will still believe his side can climb out of trouble in the closing weeks, and they still have to meet fellow strugglers Watford on 30 April. But despite beating Everton on Wednesday, Burnley's task has become more difficult after this defeat at Carrow Road.

"It was a huge setback after a huge step forward," added Dyche.

"It might come easier in a strange way when people write you off. Virtually everyone will think we're done, but we don't think that."