A point apiece means these two will meet again in the Premiership play-off quarter-finals after United’s hopes of finishing second were finally dashed.
Manager Ray McKinnon remained upbeat, saying: “If we get that wee bit of luck and keep our performance levels up, then we’ll have a good chance. We’re in a positive frame of mind going into the game on Tuesday.
“It’s just another game and we’ve got to approach it in the right manner, and we need to respect Morton. But we are in the play-offs to win it, so we’ll be back here focused.”
Bryn Halliwell, making the first appearance of his return stint with Ton, was called into action early on when he reacted quickly to deny Coll Donaldson an opener from a close-range header.
United could have gone in front on the half-hour mark but Thomas Mikkelsen’s shot smashed into the post after Halliwell got a slight touch.
Tony Andreu rattled the bar with from 25 yards and was then gifted the best chance yet when Blair Spittal, inset, found him in the six-yard box. But Andreu fluffed his shot with the goal gaping.
The home side broke the deadlock following the break when Mark Russell crossed for Kudus Oyenuga who headed firmly into the bottom corner.
United drew level when Spittal kept his cool in the box to slot the ball home and they nearly completed a turnaround when Andreu found Mikkelsen, but he was blocked by Halliwell, who went off with an injury following his save and replacement Jamie McGowan was quickly in the action to deny Spittal.
United almost grabbed all three points when Andreu blazed over, while Ton sub Aidan Nesbitt hit the post with a last-minute effort.
Morton manager Jim Duffy said: “We don’t maybe have the same strength in depth as United have, but the one thing no-one can question is our commitment and our desire and we showed that in abundance today.
“My biggest concern is the recovery period is going to be short and we are going to have to go again on Tuesday.”