In the end they lost as, quite simply, Hearts scored with their only shot on target while United could not score with numerous efforts.
The chances for United began in the 12th minute with two efforts superbly saved by Janos Balogh. Firstly, the keeper blocked a 14-yard volley from Franco Sandaza, then he stood his ground to get up and block the powerful rebound from Paul Caddis.
And the hosts continued to create the chances with Robbie Neilson's boot on the line stopping Darren Dods from opening the scoring in the 20th minute.
With both teams up for a battle as they sought that third spot, there was little more created until the 38th minute when Sandaza went down in the box after a strong push from Ruben Karipidis but the referee felt it was not strong enough to award the penalty.
The second period opened with an indecisive Hearts defence almost finding themselves in trouble twice as Sandaza almost took advantage but was unlucky on both accounts not to get a break of the ball.
And the Terrors continued to press with Warren Feeney almost grabbing the goal as he hooked the ball narrowly over from nine yards with Balogh stranded.
But it was the visitors who took the lead against the run of play with their first shot on target in the 62nd minute. His initial strike was blocked and, as the ball rebounded, he rammed it low into the net with his left foot from the edge of the box.
United, stung by this setback, threw everything at the visitors with Sandaza only a whisker away in the 77th minute.
And three minutes later, the Spaniard was rewarded for his battling efforts when he was awarded a penalty after being upended by Eggert Jonsson but his spot-kick was poor and was saved by Balogh leaving the Jam Tarts five points clear of United.