The home side established a commanding first-half lead through Lawrence Shankland – with the same player then missing a penalty – and teenager Archie Meekison who scored his first goal for the club.
Motherwell hit back in the second 45 thanks to Christopher Long but Micky Mellon's men looked like they would hold on to take all three points.
However, there was late drama as the Steelmen secured a draw in stoppage time, with Devante Cole hitting the back of the net.
United made no fewer than eight changes from the team that lost to Hibs on Saturday in the Scottish Cup semi-final at Hampden, while the Steelmen had Declan Gallagher, who has signed a pre-contract with Aberdeen, on the bench.
The home side had an early chance when Shankland latched on to a Louis Appere flick but the Scotland striker's shot was blocked by Motherwell keeper Liam Kelly.
However, the goalie was beaten in the 13th minute as Logan Chalmers hit an angled shot from just outside the box, with Shankland deflecting the ball past Kelly.
The striker then had a gilt-edged opportunity to double his tally in the 20th minute when United were awarded a penalty after Tyler Magloire brought down Appere.
Shankland stepped up to take the spot-kick but sent it wide of Kelly's right-hand post.
Motherwell were struggling to make an impact in attack with Long spurning a great opportunity as he hit a curling shot wide of the post.
The home side extended their lead in the 33rd minute when Chalmers teed up 19-year-old Meekison, who hit a bending shot from the edge of the Motherwell box that flew past Kelly before nestling in the bottom corner.
The Tangerines had another great chance in the 49th minute when Shankland produced a classy back-heel to set up Liam Smith but his low shot was tipped wide by Kelly.
The Steelmen finally dragged themselves back into the game in the 54th minute when Long made space for himself in the United box and fired a shot past United's on-loan Celtic keeper Ross Doohan.
The goalie then came to the rescue to make a vital block from a Jake Hastie shot.
However, Doohan was helpless to prevent Motherwell equalising in the 91st minute as Cole latched on to a Ricki Lamie flick to volley past Doohan.