Local hero Jay Rodriguez celebrated his England call-up with a late winner to fire the Clarets back into play-off contention.
Rodriguez struck with eight minutes to go to claim his seventh goal of the season and send him off to Italy with the under-21 squad in the perfect frame of mind.
In a landmark week it could also have been a pivotal goal for the Clarets who desperately needed all three points in their last home game for a month.
Former Norwich loan man Dean Marney had given Eddie Howe's men the lead with a peach of a goal before the break but Grant Holt's leveller 20 minutes into the second half threatened to sweep the Canaries towards another away win in their quest for automatic promotion.
Unbeaten in eight league games and with the second best record on the road in the Championship, Paul Lambert's side threw everything at the Clarets in a fiery encounter.
But Burnley and goalkeeper Lee Grant stood firm and thanks to Rodriguez made sure that City's miserable record of just one win in 16 league games at Turf Moor would get no better as they showed great character to bounce back from their miserable mid-week showing and keep the top six in sight.
Dean Marney fires Burnley in front
With new signing Marvin Bartley starting his Burnley career on the bench, Howe restricted his changes following Tuesday night's defeat at Doncaster to the recall of wideman Ross Wallace, which meant a return to a 4-4-2 formation.
And from the off the Clarets played with a greater freedom as Chris Eagles stretched the Canaries down the right wing with Tyrone Mears back to his marauding best in support.
The change also allowed Jay Rodriguez to play in a more central attacking role in support of home debutant Charlie Austin and Rodriguez almost made the switch pay-off with a goal when he headed a cross from Mears wide after ten minutes.
With Eagles swinging a succession of dangerous crosses into the City box, Burnley always looked like they were capable of puncturing the visitors' defence and it took the finger tips of goalkeeper John Ruddy to prevent one such delivery landing on the head of Austin.
Norwich's impressive away record meant they were never likely to let Burnley have it all their own way and Holt went close with a header from Leon Barnett's deep cross with half an hour gone.
Lee Grant keeps the Canaries at bay
But just as it looked as though the in-form Canaries might be starting to get their claws into the home side, the Clarets went ahead in impressive style.
Wallace started the move as he turned defence into attack with a break towards half-way and a pass into the feet of Eagles.
Eagles got Norwich on the retreat and then timed his pass perfectly to Marney, whose trademark burst from midfield ended with a perfectly placed right-foot shot into the bottom corner of the net from 20 yards to give him his second goal in three league games and the Clarets a deserved half-time lead.
Norwich had finished the first half strongly, though, and within two minutes of the re-start they had the chance to level.
Wes Hoolahan released Holt and the top scorer would have backed himself to add to his 12-goal tally but from an angle he lacked the guile to beat Grant, who saved well with his feet.
Suddenly the Clarets were facing an onslaught of yellow and green, relieved only when Wade Elliott, on for Austin to stiffen up the midfield, combined with Rodriguez and Wallace to create a chance for Marney which he dragged wide.
Chris Iwelumo goes close
Burnley dug in but with 65 minutes gone their resistance was broken when Holt made it 1-1, cleverly steering a bouncing cross from Wes Hoolahan past Grant and into the same bottom corner located by Marney.
It was now backs-to-the-wall stuff, although the Clarets had chances on the break, substitute Chris Iwelumo heading wide a cross from Eagles as the game wound up for a pulsating finish.
Norwich had made their own changes and Chris Martin had the opportunity to make a telling impact from the bench as he twice had opportunities to put the visitors in front.
But Grant, who earlier saved a Simon Lappin free-kick at full length, excelled on both occasions, first beating away the striker's shot and then forcing the substitute wide before diving to turn away his attempt to squeeze the ball home from a tight angle.
And the Clarets made the keeper's work count in dramatic style as Rodriguez pounced to grab the winner and complete a fairytale week.
And Jay Rodriguez nets the winner
The England new boy never gave the Norwich defence a moment's peace and when Danny Fox swung a free-kick beyond the far post, Rodriguez timed his run perfectly to slide the ball under Ruddy in front of his favourite Jimmy McIlroy Stand and clinch a crucial win.
Burnley: Grant, Mears, Fox, Carlisle, Duff, Cork, Marney, Wallace (Iwelumo 72), Austin (Elliott 61), Rodriguez, Eagles (Alexander 85). Subs: Bikey, Thompson, Iwelumo, Alexander, Bartley, Jensen.
Booked: Carlisle 41
Norwich: Ruddy, R Martin, Drury, Whitbread (Lappin ht), Crofts, Holt, Jackson (C Martin 62), Lansbury (Wilbraham 71), Hoolahan, Barnett, Ward. Subs: Fox, Smith, , Tierney, Steer.
Booked: Drury 16
Referee: Phil Gibbs.