With the Jambos and the Tangerines already confirmed in third and fourth places respectively, there was little more than pride to play for in this clash at Tannadice.
David Goodwillie opened the scoring after 22 minutes when he bundled the ball home from close range but Gray Glen stooped to nod home a David Templeton cross nine minutes later.
Jon Daly scored what proved to be the winner after 71 minutes when he seized upon an Ismael Bouzid error to lash the ball past Marian Kello from the edge of the area.
United gave starts to Craig Conway, Prince Buaben and Morgaro Gomis who are all set to leave in the summer.
Both teams made a bright start to the match with an inviting cross by Hearts winger Andrew Driver headed clear by Sean Dillon before Paul Dixon crossed for Daly at the other end but the Irish striker headed well wide.
United took the lead in the 22nd minute when Conway's cross was turned home from five yards out by Goodwillie.
Hearts had a chance to restore parity before the half-hour mark when Scott Robinson was fouled on the edge of the area by Dillon but Scott Pernis was equal to Craig Thomson's curling free-kick.
However, the visitors did get back on level terms with 31 minutes gone when Glen stooped to head home a cross from the lively Templeton.
United dominated proceedings after the interval and grabbed a well-deserved winner with 19 minutes remaining when Daly pounced on a loose header from Bouzid to rifle the ball into the net from 20 yards.
Source: PA
Source: PA