Graham Bayne's brilliant header earned resilient Inverness a point that keeps them in the hunt for seventh place in the Scottish Premier League.
United should have been well clear at half-time after squandering numerous chances before David Robertson's looping header found the top corner.
But Caley Thistle were much-improved after the break and grabbed a share of the points on 58 minutes through Bayne.
And the visitors could have sneaked all three points in a scrappy second half.
United had a great chance in the fourth minute when Jon Daly beat the offside trap to run on to a clever through-ball by Christian Kalvenes.
The striker beat Inverness goalkeeper Michael Fraser to the ball but his header drifted a yard wide.
The goalmouth action continued as Derek Stillie beat away Ian Rankin's powerful free-kick and Fraser was well placed to save David Robertson's lob after United broke.
Kalvenes was seeing a lot of the ball and the left-back's cross created another great chance but Fraser parried Noel Hunt's header and Collin Samuel could not react quickly enough to follow up.
United were playing some good football on the ground and Hunt cut inside after an exchange of passes between Sean Dillon and Robertson, but he could not get enough power in his left-footed shot to trouble Fraser.
Hunt sliced wide at the far post from another superb chance after Daly had got his head to a Kalvenes cross.
The hosts deservedly opened the scoring in the 42nd minute when Robertson met Hunt's cross from the right and headed into the top left corner.
Inverness came out with more urgency after the interval but the hosts had the first chance of the half when Fraser tipped over McCracken's looping overhead kick after a Dillon corner.
Caley Thistle levelled with their first real chance in the 58th minute when Graham Bayne rose brilliantly 12 yards out to head home Richie Hart's long free-kick.
Daly had a good chance to restore United's lead but Richard Hastings diverted his back-post header behind.
Dillon diverted a Darren Dods shot wide at the other end after another Hart free-kick.
And Inverness had a decent penalty claim ignored when Kalvenes collided with Bayne in the box before McBain shot wide from Hart's cutback.
The visitors were looking more likely to score going into the final quarter with nothing sticking up front for United.
Fraser almost dropped Stuart Duff's ball across goal and Craig Conway curled a cross just beyond the far post but neither side really looked like carving out a winner.
Dundee Utd: Stillie, Dillon, Wilkie, McCracken, Kalvenes, Samuel, Robertson (Duff 76), Cameron, Gomis, Daly (Conway 81), Hunt.
Subs Not Used: McLean, Mair, Robson, Easton, Goodwillie.
Booked: Daly, Gomis.
Goals: Robertson 41.
Inverness CT: Fraser, McCaffrey, Dods, Munro, Hastings, Hart (Black 86), Rankin, McBain, Duncan, Bayne, Paatelainen.
Subs Not Used: Ridgers, McSwegan, Soane, Sutherland, McAllister, Duff.
Booked: Bayne.
Goals: Bayne 58.
Att: 5,273.
Ref: S Conroy (Scotland).