Christian Eriksen came off the bench to score a 91st-minute winner for Tottenham and seal a 1-0 victory over Burnley at Wembley on Saturday.
Burnley defended resolutely and wasted time where possible, and looked to be set for a point after Joe Hart twice denied Erik Lamela.
However, Harry Kane picked out Eriksen in stoppage time, and the Dane fired beyond a helpless Hart to end Burnley's resistance in dramatic fashion.
The victory ensures Spurs remain five points behind leaders Manchester City, while Burnley are teetering two points above the relegation zone in 17th.
The wet conditions made for a sluggish start at Wembley, as a Spurs side who made five changes from the midweek draw at Barcelona found it difficult to break down Burnley's five-man defence.
However, the hosts did go close in the first half, with Lucas Moura dinking a first-time volley just wide before Lamela's stabbed effort was saved by Hart.
Kane also had a penalty claim waved away between those chances, with referee Graham Scott seeing nothing wrong with James Tarkowski's challenge on the Spurs striker.
A wayward Ashley Barnes header was Burnley's best opportunity of the half, and the forward went close shortly after the break when his volley was blocked by Toby Alderweireld and then Kane.
Burnley's tactics continued to frustrate Spurs, with Robbie Brady and Phil Bardsley both booked for time-wasting, and Mauricio Pochettino sought to bring on Eriksen and Heung-min Son to change his side's fortunes.
Hart then got down well to keep another Lamela attempt out with 15 minutes to go, but after Son fired wide from an acute angle, Eriksen finally broke Burnley's resolve with a sweeping effort at the near post.
Opta stats
- None of Tottenham's last 21 Premier League games have ended level, with Spurs winning 16 and losing five since a 1-1 at Brighton in April.
- Only Bolton in 2011-12 (18) have had a longer run without a draw from the start of a Premier League campaign than Spurs this season (17).
- Burnley failed to register a single shot on target in this match. It's the third time they've done so in the Premier League this season - no other side has done so more than once.
- Erik Lamela had 47% of Tottenham's shots in this match (7/15) and 67% of their shots on target (2/3).
The managers
Mauricio Pochettino: "We fully deserved the victory. Sometimes you don't get the reward, but we did everything to win.
"If you work hard, have patience, and try and try, you get the reward. I'm so happy for the three very important points after qualifying in the Champions League. It's a massive week for us."
Sean Dyche: "We thought it was going to be that type of game, we came down here with a solid organisation. I was pleased with the way the players delivered it tactically because it's not easy with the change of shape.
"The players have been open-minded, and they delivered it today against a top, top side, a side that create a lot of chances but didn't so much today.
Man of the match - James Tarkowski
Burnley were three minutes away from the point they were playing for, and though Spurs eventually broke them down, Tarkowski typified the visitors' dogged approach to the game.
The defender made a match-high nine clearances and three interceptions, and reduced Kane to just two blocked attempts.
Kane did get the last laugh, however, with his late assist for Eriksen, who will likely be viewed as Spurs' man of the match for his telling contribution.
The pundit - Alan McInally
What's next?
Tottenham are back at the Emirates Stadium for a mouth-watering Carabao Cup quarter-final against rivals Arsenal - live on Sky Sports - before heading to Everton in the Premier League next Sunday, also on Sky.
Burnley are also live on Sky Sports next weekend for their league match at Arsenal on Saturday.