With the Jambos and the Tangerines already confirmed in third and fourth places respectively, there was little more than pride to play.
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.
Captain Jon Daly and defenders Mihael Kovacevic and Sean Dillon both started at the expense of David Robertson, Scott Robertson and Garry Kenneth, while Keith Watson was absent after having a hernia operation on Thursday.
Hearts made six changes from the team that lost 3-0 to Celtic midweek with David Obua missing through suspension following his dismissal against the Hoops, while Marius Zaliukas, Ian Black, Ryan Stevenson, Rudi Skacel and Stephen Elliott were also left out.
In their place came Darren Barr, Ruben Palazuelos, Andy Driver, Templeton, Glen and Scott Robinson to give the visitors a youthful look.
Both teams made a bright start to the match with an inviting cross by Hearts winger Driver headed clear by Dillon before Paul Dixon crossed for Daly at the other end but the Irish striker headed well wide.
United goalkeeper Dusan Pernis comfortably stopped a well-struck volley by Hearts captain Eggert Jonsson after eight minutes before Hearts’ custodian Marian Kello made an even better stop by clawing away Goodwillie’s close-range goalbound volley.
The visitors were forced to make an early change after 21 minutes when Driver was replaced by Jason Thomson.
And within a minute United took the lead 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 Robinson was fouled on the edge of the area by Dillon but 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.
The game continued to ebb and flow with Craig Thomson and Conway both going agonisingly close with powerful long-range drives.
United had a strong penalty appeal waved away before the break when substitute Jason Thomson looked to have pulled back Daly as he tried to connect with a Conway cross.
The hosts almost made the perfect start to the second period when Kovacevic made a neat exchange of passes with Goodwillie but the Swiss defender’s effort was pushed away by Kello.
The United pressure continued with Goodwillie beating the offside trap to collect an intelligent pass from Gomis but the striker shot wide from an acute angle.
Buaben was next to try his luck but the Ghanaian midfielder failed to keep his shot from the edge of the area under the crossbar.
United got the goal their play deserved after 71 minutes when Daly pounced on a loose header from Bouzid to rifle the ball into the net from 20 yards.
Hearts searched for an equaliser but Jonsson and Templeton were both denied by Pernis in the closing stages as United held on for all three points.