Dele Alli's penalty earned Spurs a 1-1 draw at Burnley but a third winless game saw them miss the chance to cut the gap to the top four to two points.
Spurs - coming into the game on a run of four defeats in a row - were perhaps fortunate to escape Turf Moor with a point after a lacklustre opening period during which the hosts deservedly took the lead through Chris Wood's goal after a Hugo Lloris fumble (13).
Jose Mourinho made his feelings clear at the break by introducing Giovani Lo Celso and Lucas Moura, and within five minutes of the restart they were level Alli converted from the spot after Ben Mee had caught Erik Lamela (50), netting his 50th Premier League goal in the process.
Moments later Burnley were denied a penalty themselves when Davinson Sanchez barged into the back of Chris Wood and they missed a golden chance to restore their lead when substitute Matej Vydra shot straight at Lloris from clos range.
Burnley: Pope (6), Bardsley (7), Tarkowski (8), Mee (6), Taylor (7), Hendrick (7), Cork (7), Westwood (7), McNeil (7), Wood (7), Rodriguez (7).
Subs: Vydra (5), Lennon (n/a).
Tottenham: Lloris (5), Tanganga (5), Alderweireld (6), Dier (6), Sanchez (5), Vertonghen (6), Skipp (5), Ndombele (4), Lamela (6). Alli (7), Bergwijn (6).
Subs: Moura (6), Lo Celso (7), Aurier (6).
Man of the match: James Tarkowski
The draw moves Spurs four points off fourth-placed Chelsea, who still have a game in hand, while Burnley move up to 10th, with their hopes of some form of European football next season still well intact.
Half-time changes save Spurs' blushes
Mourinho had made six changes from last weekend's defeat to Wolves, telling Sky Sports ahead of kick-off he had to keep players fresh for Tuesday's Champions League last-16 second leg with RB Leipzig, but if his replacements had a point to prove they did not show it in a laborious first 45 minutes.
They could have scored inside the opening minute when Alli attempted a backheel into the path of Erik Lamela's run into the box but did not quite catch it properly, which soon turned into a fitting description of their first-half performance.
Very little the visitors attempted came off and instead Burnley produced chance after chance and won almost every battle. That nearly bought them the opening goal nine minutes in when Ashley Westwood's corner was headed back across goal by Jay Rodriguez and just the wrong side of the line before Spurs cleared.
That reprieve lasted only four minutes, with McNeil's cross cleared to Rodriguez, whose shot was spilled at the feet of Wood, and the New Zealander could not miss on his return to the Burnley line-up.
It took Spurs until the 30th minute to manufacture a first shot on target of the evening and even that was a long-range effort from Lamela, but at the other end Burnley continued on the front foot, with Westwood and Wood both going close before the break.
A clearly irate Mourinho hauled off Oliver Skipp and Tanguy Ndombele at the break, with their replacements making an instant impact as they began life on the front foot after half-time.
But there was barely time to assess their impact by the time the visitors were level, when Lamela was caught by a silly Mee challenge inside the area, and from 12 yards Alli sent Pope the wrong way.
Burnley should have had a spot kick of their own minutes later but Moss and VAR remarkably both decided against reviewing Sanchez's clear push on Wood inside his own box.
Wonderful sliding challenges at either end from James Tarkowski and Eric Dier kept the scores level, while Lo Celso's shooting radar was slightly off as he bent a 20-yard effort inches wide of the far post.
Burnley recalled the now fit Chris Wood for Matej Vydra in their one change from last weekend's 0-0 draw at Newcastle.
After a 3-2 home defeat to Wolves, Tottenham made six changes to their starting line-up.
Substitute Vydra then passed up a golden chance for Burnley to retake the lead, shooting straight at Lloris from six yards after McNeil's effort had deflected into his path, but a point still suited the hosts the better as they remain three points off the top seven, while Spurs' gap to the top four could extend to seven points by the end of the weekend.
Man of the match - James Tarkowski
Tarkowski would have looked forward to an easier night than he might have with Harry Kane and Heung-Min Son in the Spurs line-up, but he still had to be at his best to keep Pope decidedly untroubled in open play.
He made a wonderful sliding challenge to deny Lamela on the hour mark with the Argentine ready to pull the trigger and put Spurs in front, as well as making an important block on Alli's late effort and coming close to earning an assist moments before half-time, only for Wood to fluff his lines.
- Only Liverpool (48) and Manchester City (32) have earned more points than Spurs since José Mourinho's first game in charge in November (27 - tied with Wolves).
- There were nine yellow cards in this match - the joint-most in a single Premier League game this season (level with Arsenal vs Chelsea in December).
- Burnley have failed to win a Premier League game at Turf Moor despite scoring the opening goal for the first time since December 2018 vs Liverpool (1-3) - they had won 11 games in a row from such a position.
- Burnley defender Ben Mee has given away five penalties in the Premier League in his career, at least three more than any other Burnley player.
- Dele Alli became the seventh player to reach 50 Premier League goals for Spurs - only Harry Kane (23 years 44 days) reached this milestone at a younger age for the club than Alli (23 years 331 days).
Burnley travel to Man City at 3pm next Saturday, while Tottenham visit RB Leipzig in the Champions League on Tuesday at 8pm.