Both Leeds and Burnley are embroiled in a fight for survival and the Clarets' latest result helps the Whites in their bid to secure safety.
Harry Kane's penalty on the stroke of half-time was enough to seal all three points for Champions League-chasing Spurs.
The award of Kane's penalty was a contentious decision and needed to be referred to the Video Assistant Referee after a handball was spotted inside the Burnley penalty area.
Ashley Barnes was deemed to have handled the ball as it brushed past his outstretched arm, and referee Kevin Friend - after consulting the pitchside monitor - pointed to the spot.
Burnley goalkeeper Nick Pope was in inspired form at the Tottenham Hotspur Stadium, but was left rooted to the spot as Kane's spot-kick was converted.
The officials' decision sparked fierce remonstrations from the Burnley coaching staff, which spilled over into the tunnel as the two sides retreated back to the dressing rooms at the break.
It leaves Burnley with two games remaining, only ahead of Leeds in the Premier League table on goal difference.