John Rankin headed the visitors ahead midway through the second half after Robbie Muirhead's effort had struck the bar.
However, Murray Davidson pulled Saints level to earn his side a point and keep them level on points with United.
A point apiece seemed a fair outcome but Saints captain Dave Mackay will rue his first-half penalty miss.
That could have proved decisive, not only in terms of the match but also in the league table, with fourth spot still potentially good enough for a Europa League place if Inverness Caledonian Thistle win the Scottish Cup.
But Mackay's spot-kick was too close to Radoslaw Cierzniak after Michael O'Halloran had been brought down by Callum Morris.
That was about the closest thing to a goal in the first period, although Nadir Ciftci's amazing effort from 35 yards, which came back off the post, was worthy of better.
So closely contested was this game that a goal-less draw looked on the cards until Rankin was quickest to react after Muirhead's header had come back off the bar.
But the visitors' joy was short-lived as former United midfielder Danny Swanson swung a cross in from the left and Davidson guided a volley past Cierzniak.
Both sides pressed for a winner, but neither could quite craft an opening of sufficient quality, ensuring the battle for fourth will go to the wire.
The Tangerines hold a three-goal advantage over the Perth men, with both sides on 53 points.
Saints visit Celtic on Friday, with United travelling to take on Inverness on Saturday.