Gylfi Sigurdsson’s magnificent long-range free-kick frustrated Jose Mourinho’s hopes of a top-four finish in yet another Old Trafford stalemate.
For the sixth time in eight home games in 2017, United drew despite being gifted a first half opener after Wayne Rooney claimed his first home league goal of the season from a harsh penalty award.
But after 78 minutes Rooney fouled Jordan Ayew nearly 25 yards from goal and, after a lengthy period of United preparations, Sigurdsson stroked home a superb finish that left David de Gea rooted to the spot.
Victory would have lifted United into third place, temporarily at least, and not even a new club record of 25 top-flight games unbeaten in a single season could ease the frustration that was compounded by injuries to Luke Shaw and Eric Bailly.
Rooney struck a penalty in the third minute of first half injury-time, following much deliberation by referee Neil Swarbrick after Marcus Rashford went down under a challenge from goalkeeper Lukasz Fabianski - a decision hotly disputed by the visitors.
The recalled United club captain made no mistake with a clinical delivery from the spot kick and the struggling visitors could feel hard done by after an impressive first half display.
Jose Mourinho’s plans were not aided by an early injury to year another defender - this time the injury-prone England left-back Shaw who appeared to injure his ankle with no opponent near him after just seven minutes.
United should have been behind before the game was even 15 minutes old. First, Ayew’s shot was blocked by Bailly who then cleared the rebound against the legs of Sigurdsson and watched in relief as the ricochet flew behind.
Then, after 13 minutes, Tom Carroll found Fernando Llorente, who beat Bailly far too easily and saw his curling shot kept out by de Gea’s flying save.
Sigurdsson also tested de Gea with one of his trademark set-pieces, a 25-yard free-kick which the Spanish keeper caught by diving sharply to his left.
By then, United had at least gained a foothold in the game and offered opposition goalkeeper Fabianski some minor discomfort.
On 16 minutes, Anthony Martial’s decent through ball picked out Jesse Lingard’s well-timed run although the youngster’s left-foot volley lacked power and was turned around the post by the Swansea keeper.
And soon after Ashley Young was the architect as he worked his way skillfully down the left before crossing for Rooney who, at full stretch, was only able to head over the goal.
Martial maintained the pressure on the half-hour when he cut in from the left and into the Swansea area from where he produced a right-foot shot which Fabianski stopped, smothering the ball just in time to deny Lingard a sniff of the rebound.
But, after a period of resolute defensive duties, Swansea launched another impressive attack when Carroll played through Ayew whose shot was saved by the outstretched leg of de Gea with the rebound flying tantalisingly close to a pair of white-shirted attackers.
The early intensity had dipped by the time the interval approached as Lingard ended the period with a lazy shot wide from the edge of the area before Rooney’s opening goal.
Rooney showed his lack of match sharpness early in the second half when he passed up the opportunity to claim what could have been a decisive second goal, striking team mate Martial from eight yards.
Swansea almost capitalised as a dangerous Sigurdsson free-kick found Llorente but his header lacked direction and Mourinho’s concerns mounted on the hour when Bailly limped out of the game with what appeared to be a hamstring problem.
Martial might have improved Mourinho’s mood soon after with a powerful shot which took a treacherous deflection before being kept out impressively by Fabianski who shifted his weight and stuck out a leg.
As Clement chased the game, Swansea also ran into injury problems with substitute Jefferson Montero managing to survive just six minutes before being stretchered off.
And United almost added to their concerns after 75 minutes when Herrera picked out the overlapping Antonio Valencia whose powerful shot was parried by Fabianski.
Even after their equaliser, Swansea still pushed for a winner, however, and Llorente should have done better than mis-kick close to goal from another threatening Sigurdsson set-piece.