Neither side so much as had a shot on target until James Trafford palmed over Dan James' 88th-minute effort for Leeds as Burnley recorded a fourth 0-0 draw in their past five home games, and their ninth goalless stalemate of the season.
Billed as a battle of attack versus defence between Daniel Farke's high-scoring Leeds side and Scott Parker's defensive specialists, it was the latter that prevailed as Burnley have now gone more than 10 and a half hours since last conceding, having only let in nine goals in 29 league games all season.
The draw saw Leeds edge two points clear of Sheffield United at the top of the table, while Burnley remain third, a point shy of the Blades.
There had been some early encouraging signs for Leeds as Jayden Bogle and then Brenden Aaronson found space to run through the midfield, but it would not last as Burnley quickly tightened up and shut down the middle of the park.
Leeds had half a penalty claim before the break when Sam Byram ran on to a diagonal ball from James and went sprawling, but referee Josh Smith was happy Anthony's shoulder barge was fair.
The half ended with neither goalkeeper having been tested, but if the first 45 minutes had been low on goal-mouth action, it somehow got worse after the break.
Both sides struggled to break down the other as strong winds and relentless rain had an impact on an increasingly scrappy contest.
Both managers made changes seeking a spark. Mateo Joseph and Largie Ramazani replaced Manor Solomon and Joel Piroe for Leeds, before Parker sent on Brighton loanee Jeremy Sarmiento in place of Lyle Foster.
Leeds roused themselves late on, with Bogle cutting into the box, but his shot was blocked by Josh Cullen. From the resulting corner the ball came out to James, but his rising half-volley was pushed over by Trafford.
It proved the only attempt on target of a disappointing match.
