A late strike from Craig Dargo gave the home side all three points at the Caledonian Stadium.
A disappointing first half was spoiled by a swirling wind which did little to allow quality football.
Dargo came close to giving Inverness the lead but his shot was cleared off the line at the second attempt by Charlie Mulgrew.
However, Dargo was not to be denied as he fired home a left-footed strike from 12 yards out in the dying seconds.
A pedestrian start hampered by the strong wind around the stadium yielded little enterprising football, until Mulgrew bent a sixth-minute free-kick just past Inverness goalkeeper Mark Brown's right-hand post.
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Caley eventually mustered a shot on goal in the 18th minute when Liam Keogh's chip across the pitch found Richie Hart lurking on the edge of the penalty area.
However, the midfielder's controlled shot produced a fine save from Samson.
Hart was then able to find the unmarked Keogh with a free-kick and the ex-Celtic youngster tried his luck with a shot from 25 yards.
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The drive was flying well off course until the intervention of Ross Tokely, who sent the ball up into the air allowing Darren Dods a header at goal.
In the 52nd minute, Dargo was able to send a shot towards goal from Hart's corner, but, fortunately for the visitors, Mulgrew was stationed at the back post and, at the second attempt, cleared the ball off the line.
The on-loan Celtic player was at the heart of the action for United and, from his cross, David Robertson was able to direct a header at goal which may have troubled Brown had it not been for the intervention of Dods.
Inverness responded with a shot from Dennis Wyness from 18 yards which curled just wide, before Barry Wilson's inswinging cross curled right across the face of goal when the merest of touches would have sent the ball into the net.
Seven minutes later, Brown made a good save from Mulgrew's free-kick, before Dargo capitalised on poor play from Alan Archibald two minutes into stoppage time to score the winner with the last kick of the match.
Booked: Tokely.
Goals: Dargo 90.
Dundee Utd: Samson, McCracken, Archibald, Ritchie, Gardiner, Duff, Kerr, Brebner (Abbot 85), Mulgrew, Samuel, Robertson (Goodwillie 75). Subs Not Used: McLean, Kenneth, Cameron, Callaghan, Easton.
Booked: Kerr, Ritchie.
Att: 3,609
Ref: M Tumilty