Barry Wilson scored with the last kick of the game to keep alive Inverness' push to finish in the top six of the Bank of Scotland Premier League.
Caley Thistle almost broke the deadlock just before the break when Richard Hastings' header was cleared by Mark Kerr, while United substitute Collin Samuel should have scored with a header in the 69th minute.
In a dramatic conclusion Grant Munro was dismissed in his 200th appearance for Inverness following a foul on Barry Robson, before Wilson struck at the death.
In a tetchy start to the game, United enjoyed more of the early possession, but were only able to create one chance and that came in the third minute.
Lee Wilkie sent an excellent pass out to Sean Dillon who had made his way up the touchline and the right-back immediately directed a cross into the home penalty area.
The ball was met by the right foot of Jon Daly but the striker could only flick his effort wide of goal.
Play soon became congested in the middle of the park where a heated battle between Russell Duncan and Robson gathered steam.
Following a foul by Duncan on Robson, the United captain swung a free-kick towards the Inverness goal where Wilkie tumbled to the deck after tussling with Darren Dods.
Referee Stephen Finnie chose to penalise Wilkie though, much to the defender's annoyance.
In the 21st minute visiting goalkeeper Derek Stillie was eventually called into action in order to deal with a half-volley from Wilson, while at the other end Michael Fraser did well to push a Robson shot around his far post.
Ross Tokely then headed over from John Rankin's corner while Noel Hunt flashed a drive just over the bar following Daly's flick.
Those opportunities did little to mask a dull game though, which was finally brought to life four minutes before the interval courtesy of a tremendous surge forward by the sprightly Wilson.
The former Livingston player did well to clip a cross towards the back post which was met by Hastings and the left-back's header was only stopped by the timely intervention of Kerr.
Two minutes after the restart the visitors were presented with a great opportunity to end the stalemate but Hunt's header went wide when he should at least have tested Fraser.
Caley Thistle retaliated with a low Rankin drive which was comfortably gathered by Stillie, while in the 62nd minute Hunt again got too much purchase on an effort from close range.
United then took an aerial route towards goal only for unmarked substitute Samuel to miss a glorious opportunity, sending his downward header wide after meeting a great cross from Christian Kalvenes.
With 14 minutes remaining Samuel came close to atoning for that miss when he shot wide, before Duncan flashed a curling shot from 25 yards past a stranded Stillie's far post.
That scare came as a wake up call to United and with five minutes remaining Fraser did brilliantly to parry a shot from Robson, before the United captain was on the receiving end of a cynical challenge from Munro for which the Caley Thistle defender saw red.
It was 10-man Inverness who went on to win all three points though. After Wilson's initial drive was saved by Stillie, Graham Bayne and Markus Paatelainen worked the ball back into the path of the veteran forward who scored with a well-placed shot.
Teams
Inverness CT Fraser, Tokely, Dods, Munro, Hastings, Wilson,Black, Duncan, Rankin (Paatelainen 73), Bayne,McAllister (McSwegan 64).
Subs Not Used: Ridgers, McCaffrey, Hart, Morgan, Sutherland.
Sent Off: Munro (90).
Booked: Black, Duncan.
Goals: Wilson 90.
Dundee Utd Stillie, Dillon, McCracken, Wilkie, Kalvenes,Robertson (Samuel 46), Kerr, Gomis, Robson, Daly (Robb 73),Hunt (Goodwillie 81).
Subs Not Used: McLean, Mair, Watson, McCord.
Booked: Kalvenes.
Att: 3,901
Ref: S Finnie (Scotland).