United's relegation-battling rivals Burnley were on course to net a precious three points in the club's first game since Sean Dyche was sacked after Wout Weghorst's 33rd-minute header put the Clarets 1-0 up in Sunday's game at West Ham United.
But the third-bottom Turf Moor outfit then squandered a glorious chance to double their advantage when Maxwel Cornet sent a penalty wide at the end of the first-half.
The Irons again struggled to break the Clarets down after the interval but the Hammers drew level with 16 minutes left as the unmarked Tomas Soucek converted from Manuel Lanzini's free-kick, handing Leeds a boost in the process.
The Hammers then pushed hard for a winner but visiting 'keeper Nick Pope pulled off a series of brilliant late saves.
Burnley are now eight points behind fifth-bottom Leeds having played just one less game.
The Clarets are three points adrift of fourth-bottom Everton who have played one game less than the Clarets and host Leicester City on Wednesday night.
Leeds are five points ahead of Everton but the Toffees have two games in hand on them.
Sunday's contest at the London Stadium was marred by a serious injury to Burnley midfielder Ashley Westwood in the first-half.
Westwood suffered a serious injury whilst challenging for the ball with West Ham's Nikola Vlasic who was visibly upset after the Clarets player had gone to ground.
Westwood immediately signalled for help and was quickly consoled by his concerned Clarets team mates.
After a lengthy stoppage, Westwood was stretchered off to applause from both sets of players.
The contest was Burnley's first game since the club decided to sack boss Dyche after ten years in charge.
Mike Jackson, the club's under-23s boss, is in temporary charge, assisted by Academy director Paul Jenkins, under-23s goalkeeping coach Connor King and club captain Ben Mee.
Elsewhere on Sunday, Newcastle United booted 12 points clear of the drop zone with a last-gasp 2-1 win at home to Leicester City.
The Magpies are now 14th, four points ahead of Leeds on the same number of games played.