Micky van de Ven's late goal has kept Tottenham's Champions League hopes alive, but their 2-1 win condemned Burnley to Premier League relegation.
Both teams needed a win for their respective battles at either end of the table, and Jacob Bruun Larsen's goal (25) gave the Clarets hope of three points.
But in an even first half, a fine solo effort from Pedro Porro (32) gave Tottenham an equaliser soon after.
Spurs dominated the second half, but it took an 82nd-minute strike from Van de Ven to secure their victory.
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The win sees Tottenham close the gap to four points on Aston Villa, who face Liverpool on Monday Night Football. But Unai Emery's side will secure fourth spot if they win that game, meaning Spurs will miss out on Champions League football for next season.
Burnley now know they will be playing back in the Championship next term, with the defeat seeing them relegated with a game to play.
How Tottenham saw off Burnley
Both sides could have gone ahead in the first 10 minutes. Guglielmo Vicario kept out a chances from Vitinho and Lyle Foster, while Aro Muric stopped Brennan Johnson's placed effort.
And the first-half goals came in a pendulum too. Burnley opened things up with a fine goal, starting when Sander Berge nipped past Porro in midfield. He then found Bruun Larsen who slotted home.
Six minutes later, Tottenham were level. Johnson tapped the ball into Porro's path, and it was a fine solo run from the defender into the area before firing home with a thunderous effort.
Despite a good start to the second half from Spurs, Burnley went close again around the hour. Wilson Odobert fired over, before Maxime Esteve looped a header onto the top of the net. At the other end, Muric made a fine save from close range to keep out James Maddison.
Tottenham kept trying - and failing - to score a second. The pick of them came in the 78th minute as Johnson somehow poked a fine Heung-Min Son cross wide from point-blank range. Soon after, Muric kept out Pape Sarr's effort to keep Burnley in the game.
The decisive goal came from an unlikely source in Van de Ven. Substitute Dane Scarlett did well to open up the space for his team-mate, who took a great first touch before slotting home into the far corner.
Ange: More to come from Spurs
Tottenham manager Ange Postecoglou to Sky Sports:
"Credit to the players, we've had four defeats and it's bound to have some stress and anxiety into the performance. Burnley had nothing to lose today, they had to go for it.
"For the most part, we handled it pretty well. The football was decent, but in the first half, we lacked a bit of conviction in the final third. Second half, we were outstanding. Their goalkeeper had an unbelievable game and they did some desperate defending.
"The pleasing thing for me is the lads worked their way through it and got the result.
"Almost every game, we finish strong, we've just let [the last few] games get away from us. We hung in there today, the goal before half-time was important from Pedro and we were always confident we'd finish strong.
"It took two defenders to score for us today, but it's a sign of our development as a team.
"For a lot of these players, it's their first year in the Premier League, like Micky. There's so much more in these guys. Most of these players we've given the experience to this year, that's the exciting bit. We'll strengthen in the summer and I'm sure there'll be great growth in us.
"We've still got six points to play for and we'll see where that takes us."
What's next for Burnley?
Burnley manager Vincent Kompany to Sky Sports:
"No sulking, no feeling sorry for ourselves. We worked hard, we tried everything and we gave ourselves a chance.
"I felt that we took the game how we should have done. This season was a tough one because of the levels of the Premier League, but in the last two months, we've been a really exciting team. it's unfortunate, but the excitement in terms of the clubs and players remains.
"We have to prepare for next season. Day one is tomorrow and that's about where the opportunity is to get back to the Premier League as soon as we can.
"The hardest thing for me is I don't know if it will ever be appreciated how committed the players have been this year, how committed the club has been. We've not rewarded ourselves enough for the hard work.
"At the end of the day, maybe my biggest frustration is that we haven't been able to get the rewards for the work the boys have done. Then maybe it would be more appreciated how exemplary they have been this season.
"The main thing for me is I don't want to hear any complaints, hear any sulking. Tomorrow is exciting because w get to prepare for another exciting season and get to hopefully put ourselves in a position as soon as we can to have another go at this league. That's important for a club like us."
Opta stats - Van de Ven only scores winners
- Tottenham have rescued 25 points from losing positions in the Premier League this season, their most in a single campaign in the competition (previously 24 in 2010-11). Indeed, only Liverpool (28) have come from behind to win more points in the Premier League this term than Spurs.
- Since their debut Premier League campaign in 2009-10, no side has been relegated from the top-flight on more occasions than Burnley (4 times, level with Norwich), facing the drop in 2009-10, 2014-15, 2021-22 and now 2023-24.
- All three of Micky van de Ven's Premier League goals for Tottenham this season have been winners, also netting against Luton in October and Nottingham Forest last month.
What's next?
The Premier League's final day will take place on Sunday May 19 with all games kicking off at 4pm. Tottenham head to Sheffield United, while Burnley host Nottingham Forest.
Before that, Spurs take on Man City at the Tottenham Hotspur Stadium on Tuesday May 14, live on Sky Sports; kick-off 8pm.
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