Match ends, Burnley 0, Tottenham Hotspur 0.
Harry Kane captained Tottenham for the first time but was unable to continue his prolific scoring run in a disappointing draw at Burnley.
Kane replaced injured goalkeeper Hugo Lloris as Spurs skipper as he looked for his 30th goal of the season to help keep alive his side's top-four hopes.
But Burnley nullified his threat and went closest to winning when Danny Ings shot straight at Michel Vorm early on.
The Clarets remain in the bottom three, two points adrift of safety.
Liverpool's 4-1 defeat by Arsenal the day before had given Tottenham the opportunity to move above them into fifth place and put some pressure on Manchester City before the defending champions' trip to Crystal Palace on Monday (kick-off 20:00 BST).
At the other end of the table, the incentive to try to secure all three points was just as great for Burnley as they kicked off knowing victory would take them out of the relegation places.
But neither side was able to produce the quality needed to make the difference in a surprisingly low-key game.
That did not promise to be the case when Ings was presented with an excellent opportunity after just five minutes.
George Boyd's tackle on Ryan Mason released Burnley's top scorer but as he burst into the box he could not beat Vorm.
The former Swansea keeper made his first Premier League start in place of Lloris, who was ruled out with a gashed knee he sustained in Tottenham's win over Leicester last month.
Vorm also needed to tip over another effort from Ings just before the break as the Clarets striker looked to move to double figures for the season.
But that apart, neither goalkeeper was forced to make a meaningful save with Kane, who had scored 11 goals in his last 11 club games and also netted on his England debut against Lithuania on 27 March, often looking isolated and failing to register a serious shot on target.
Tottenham's previous games this season had featured a total of 95 goals but the lack of one for Mauricio Pochettino's side further dented their slim prospects of qualifying for the Champions League as they played out their first goalless draw away from home in the Premier League since November 2013.
Burnley, who had one further late chance to secure a second win in 10 league games when Boyd nodded wide from a Lukas Jutkiewicz pass in injury time, have been short of goals with just one in their last five games.
But Sean Dyche's side did keep a second successive clean sheet at Turf Moor, having beaten Manchester City 1-0 in their previous home game, and they climbed back above QPR and within two points of Aston Villa in 17th place.
Burnley manager Sean Dyche told BBC Sport:
"It was a strange game and that sometimes happens when the sun shines out of nowhere - especially up here.
"Every point is vital and it's a clean sheet against a good side. Sometimes you've got to be realistic and accept that.
"We're not disappointed. We went for the win and created chances that could have won the game.
"I felt we probably edged it and if there was going to be a winner it would probably be us.
"We kept them very quiet and that's two clean sheets out of three so there's life there.
"We have a very motivated group of players who want to stay in the Premier League and that was evident again today."
Tottenham manager Mauricio Pochettino told BBC Sport:
"If you want to play in big things you need to win games. But Burnley are a very tough team and made it difficult.
"We had to fight and created some chances but not enough to win the game.
"It's true that we maybe lacked patience to create some more chances but that can happen sometimes.
"You always need to win at a club like Tottenham. We know it will be difficult (to reach the top four) but we will try."
- 2TrippierBooked at 68mins
- 6MeeBooked at 78mins
- 9VokesSubstituted forJutkiewiczat 76'minutes
- 2WalkerSubstituted forDaviesat 47'minutes
- 38MasonSubstituted forTownsendat 83'minutes
- 22ChadliSubstituted forLamelaat 64'minutes
- Martin Atkinson
- Shots on Target
Second Half ends, Burnley 0, Tottenham Hotspur 0.
Ben Davies (Tottenham Hotspur) wins a free kick in the defensive half.
Foul by Lukas Jutkiewicz (Burnley).
Attempt missed. George Boyd (Burnley) header from the right side of the six yard box is close, but misses to the left. Assisted by Lukas Jutkiewicz with a headed pass.
Offside, Burnley. Ashley Barnes tries a through ball, but Danny Ings is caught offside.
Attempt missed. Nabil Bentaleb (Tottenham Hotspur) left footed shot from outside the box misses to the right following a corner.
Corner, Tottenham Hotspur. Conceded by Ben Mee.
Substitution, Tottenham Hotspur. Andros Townsend replaces Ryan Mason.
Offside, Burnley. Ben Mee tries a through ball, but Lukas Jutkiewicz is caught offside.
Attempt blocked. George Boyd (Burnley) left footed shot from the left side of the box is blocked. Assisted by Kieran Trippier with a cross.
Corner, Burnley. Conceded by Ben Davies.
Attempt blocked. Lukas Jutkiewicz (Burnley) right footed shot from the right side of the box is blocked.
Paulinho (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Scott Arfield (Burnley).
Offside, Tottenham Hotspur. Christian Eriksen tries a through ball, but Paulinho is caught offside.
Ben Mee (Burnley) is shown the yellow card for a bad foul.
Erik Lamela (Tottenham Hotspur) wins a free kick on the right wing.
Foul by Ben Mee (Burnley).
Substitution, Burnley. Lukas Jutkiewicz replaces Sam Vokes.