Colin Nish broke the deadlock after 12 minutes with a weak shot that United goalkeeper Dusan Pernis should have saved.
And the Hibs striker scored his second with a diving header after 72 minutes to ensure his side finished the season on a high.
The win coupled with Motherwell's 3-3 draw against Rangers at Ibrox guaranteed a place for John Hughes' side in next season's Europa League.
With next week's Active Nation Scottish Cup final against Ross County in mind United made six changes with goalkeeper Pernis, Jennison Myrie-Williams, Pavels Mihadjuks, Andis Shala, Damian Casalinuovo and Kevin Smith all handed starts.
On-loan defender Andy Webster and Prince Buaben missed out with Jon Daly, Craig Conway, David Goodwillie and Scott Robertson on the bench.
Hibs' only change from their crazy 6-6 midweek draw against Well saw Sol Bamba replace Paul Hanlon following his return from suspension with Ivory Coast manager Sven-Goran Eriksson rumoured to be at Tannadice to watch the defender ahead of this summer's World Cup.
The visitors should have taken the lead inside two minutes when a lapse of concentration from Garry Kenneth put Anthony Stokes through on goal but the Irishman shot weakly at Pernis.
Derek Riordan was next to test the Slovak stopper with a tame free-kick from the edge of the area before the Hibees broke the deadlock after 12 minutes.
Midfielder Liam Miller crossed for Nish whose first-time effort rolled under Pernis and into the net.
The Tangerines almost restored parity four minutes later when Kenneth headed Danny Swanson's corner goalwards but David Wotherspoon was perfectly placed on the line to clear the ball to safety.
Myrie-Williams was looking United's most promising route to goal in the opening period with several darting runs, however Graeme Smith in the Hibs goal was rarely tested.
The visitors could have doubled their advantage seven minutes before the interval when Nish released Stokes but Pernis was equal to the striker's low drive.
United almost levelled on the stroke of half-time but Casalinuovo's diving header from a clever David Robertson free-kick found the side-netting.
Hibernian made a change in first-half added time when Kevin McBride replaced the injured Miller.
United shuffled their pack at the break with Scott Robertson replacing Mihadjuks with Sean Dillon moving into the centre of defence to partner Kenneth.
John Rankin went painfully close to adding a second for Hibs when his low drive struck Pernis' left-hand post after 49 minutes.
Peter Houston introduced Greg Cameron for Swanson and Ryan Dow for Kevin Smith before Shala went close with a header from close range that was well saved by Graeme Smith.
Cameron immediately went into the book for a late tackle on McBride after 66 minutes before Alan Gow, who had replaced Anthony Stokes, curled the ball over the bar as the visitors looked for a second to kill the match as a contest.
And the second goal arrived after 72 minutes when Steven Thicot's cross was headed home by in-form striker Colin Nish, who had scored a hat-trick against Motherwell midweek.
Kenneth, United captain for the day, should have pulled a goal back but the defender failed to keep his header under the bar from Dow's corner.
But Hibernian held out for all three points and can look forward to European football next term.