Norwich had two players sent off as a Chris Wood strike and a Ben Godfrey own goal kept Burnley in European contention with a 2-0 win at Carrow Road.
The relegated Canaries, who had come close to frustrating Chelsea at Stamford Bridge earlier in the week, started encouragingly but shot themselves in the foot when Emi Buendia was dismissed by VAR for aiming an elbow at Ashley Westwood (36), before Josip Drmic followed him down the tunnel for a late challenge on Erik Pieters (45).
Burnley then compounded the hosts' nightmare first half when Wood grabbed his 13th league goal of the season with an overhead kick from Johan Gudmundsson's cross moments before the interval.
After half-time, the Clarets struggled to build the intensity to regularly test Tim Krul despite their two-man advantage, but were handed a stroke of good fortune when Godfrey controlled Pieters' cross beyond his goalkeeper (80), to confirm a miserable afternoon for the hosts in their final home game ahead of their impending relegation - as well as a ninth consecutive defeat.
Norwich: Krul (7), Aarons (6), Godfrey (5), Klose (6), Lewis (6), Cantwell (5), Tettey (6), Buendia (4), McLean (5), Hernandez (5), Drmic (5).
Subs: Zimmermann (6), Rupp (6), Idah, Vrancic (n/a).
Burnley: Pope (7), Bardsley (6), Tarkowski (7), Long (6), Pieters (7), Gudmundsson (7), Westwood (7), Brownhill (6), McNeil (6), Wood (7), Rodriguez (6).
Subs: Brady (6), Vydra (7).
Man of the match: Chris Wood
Burnley, the first of the teams in European contention to play their penultimate game, rise to ninth, a point off seventh-placed Tottenham in the final Europa League qualifying spot, albeit with a vastly inferior goal difference, while goalkeeper Nick Pope's 15th clean sheet of the season sets him ahead of the trailing pack in the race for the Golden Glove.
Norwich prove own worst enemies as Burnley march on
Previously porous Norwich had shown against Chelsea in midweek they could put on a defensive display when required, but having failed to register a single shot on target in west London, improvements were needed at the other end of the pitch.
On the early evidence, they looked like being realised. Twenty minutes in, Godfrey's header from a corner was kept out by a smart stop from Pope, before James Tarkowski diverted Alexander Tettey's effort on the rebound behind with a vital block.
But any hope of showcasing how the Canaries can bounce back from the Championship next season was dealt a blow 33 minutes in. Westwood put an arm around Buendia's waist as the recalled midfielder looked to get away, and in response was met with a blow to the head from his elbow.
While the Burnley man clearly made the most of the contact, VAR left the ultimate decision up to on-field referee Kevin Friend, who went to his back pocket to dismiss Buendia after reviewing the incident on the pitch-side monitor.
"It's unnecessary, no doubt about that and he can't have too many complaints," said former Canaries forward and Sky Sports pundit Efan Ekoku.
Emi Buendia returned for Norwich for Luka Rupp, with Teemu Pukki again named on the bench.
Burnley also made one change, bringing in Johann Gudmundsson for the injured Charlie Taylor.
One red became two in first-half injury time when Drmic, perhaps out of frustration, flew into a challenge on Pieters, and while he did not make significant contact with the defender, could not have too many complaints about following his team-mate down the tunnel.
Worse would follow still before the break as Gudmundsson recycled a wasted cross by finding Wood on the far side, and his overhead kick snuck in at Krul's near post to add insult to injury on a nightmare 14 minutes for the hosts.
After half-time, and a personnel change from Daniel Farke, it appeared it would be a matter of how many Burnley would score - and Wood could have doubled his tally within minutes of the restart but sliced Westwood's excellent diagonal pass well wide.
However, while Norwich remained compact with two banks of four, Burnley did nowhere near enough to stretch the beleaguered hosts and it took more than 20 minutes for them to pull another save out of Krul, who turned Jay Rodriguez's shot behind after a deflection from Christoph Zimmermann.
In fact, it would need a helping hand from the Canaries to eventually double the lead. Pieters' ball into the near post was misjudged by Godfrey, whose first touch took it past his goalkeeper to compound a miserable afternoon.
Another pair of quick-thinking saves from Krul kept the scoreline respectable late on, but both sides were happy to hear the full-time whistle on yet another tough afternoon for Norwich, and a seventh game unbeaten for their visitors.
Man of the match - Chris Wood
There were few stand-out performances at Carrow Road but Wood's was the one that showed the quality to break the deadlock.
He was typically combative too, winning six aerial duels against Timm Klose and Christoph Zimmermann, and perhaps should have had another goal but missed a presentable second-half opportunity.
- Norwich are just the third team in English top-flight history to lose five consecutive home games without scoring a single goal, after Sheffield Wednesday (April 1920) and Birmingham City (February 1922).
- Since the restart last month, only Manchester City (18) and Manchester United (17) have earned more Premier League points than Burnley (15 - W4 D3 L1).
- Burnley extended their unbeaten run in the Premier League to seven games (W4 D3) - only Manchester United are currently on a longer active streak (12).
- Norwich are the first team to have multiple players sent off in the first half of a Premier League game since August 2015 (two Stoke red cards v West Brom).
Norwich will end their season-long Premier League stay by visiting Manchester City on the final day, next Sunday, at 4pm.
The curtain will come down on Burnley's campaign with a home game with Brighton at Turf Moor at the same time.