The Whites defense and the play of goalkeeper Ilian Meslier frustrated the visitors as Leeds are now on 47 points, ninth in the Premier League as they eye a top-half finish while the Red Devils remain second with 67 points, second behind rivals Manchester City.
Story of the match
Manchester United had an early chance in the second minute as Bruno Fernandes delivered to the head of Mason Greenwood, his effort straight into the gloves of Ilian Meslier.
Shortly after, Victor Lindelof spotted Marcus Rashford and his first touch killed the ball dead, but his second was dragged well wide of the right-hand post.
More pressure from the visitors as Fernandes delivered a free kick low into the Leeds area, but Harry Maguire failed to adjust properly to re-direct the shot off his knee on target.
Leeds had a shout for a penalty in the 19th minute as Jack Harrison's cross was behind Patrick Bamford, but Luke Shaw appeared to lean in with his arm. After a check from VAR, referee Mike Dean failed to give it.
Fernandes was causing more problems for the home sides' defense and he played a neat one-two with Daniel James, but Greenwood's poor touch from the cut-back saw the chance wasted.
On the half-hour mark, Fernandes was fouled by Kalvin Phillips with his back to goal, but his free-kick floated harmlessly over the Leeds crossbar.
The tables were turned in the 34th minute as Fernandes was caught out by Phillips, who worked it to Stuart Dallas, but his low, left-footed shot was straight at United goalkeeper Dean Henderson.
Bamford was alert to clear Fernandes' free-kick over his own bar after Luke Ayling had slipped. Shaw then took the visitor's next free-kick, which just eluded both Maguire and Fernandes.
On the stroke of halftime, Meslier made a brilliant save as he made a one-handed stop of Rashford's powerful strike and Maguire sent the ensuing corner over.
In the 51st minute, United picked up where they left off as Shaw's throw-in is to Fernandes. His dummy led to a shot that was cleared by two Leeds defenders.
Fred then picked out Greenwood, played onside by Ezjgan Alioski, but his shot was gathered in by Meslier. Alioski then prevented James from getting a shot off after some great build-up play by Fernandes and Rashford.
Subsitute Mateusz Klich had Leeds' first chance of the second half as in the 74th minute as Bamford played him through, but his shot lacked conviction and was straight at Henderson.
The Red Devils shot-stopper then had to make a brilliant double save from Ayling and at the other end, six minutes from time, Paul Pogba fed Greenwood, his effort straight at Meslier.
In the 88th minute, a corner from the visitors was cleared to Fernandes, but he could only clip the ball straight at the Leeds 'keeper. Robin Koch then cleared Greenwood's 90th-minute chance.
That was all as the game, lacking in anything of the way of cutting-edge. came to an end, both teams eager to move on after a match that no one will want to remember.
Man of the match: Kalvin Phillips
No one really deserves this honor as there was no one who stood out, but since I have to put someone here, the Leeds midfielder gets the nod. He made three key passes, recorded eight tackles and was physical with Manchester United's key players in the big moments.
No cutting edge either way
Manchester United held 55 percent of the possession as well as a 15-6 edge in shots, but couldn't find that one moment of brilliance, were poor in the final third and really didn't trouble Meslier. Henderson only needed to make three saves and none of them were difficult. A poor game all around.
The title race is all but over
If it wasn't already, Manchester City have one hand on their third title in four years. United really needed to win this game and hope their fierce rivals slipped up somewhere, but this draw all but confirms the trophy will be headed back to the blue half of Manchester.