Graham Bayne's brilliant header earned resilient Inverness a point which keeps them in the hunt for seventh place in the Bank of Scotland Premier League.
Dundee United should have been well clear at half-time after squandering numerous chances before David Robertson's looping header found the top corner.
But Bayne rose highest to head a 58th-minute equaliser from his side's first real chance and the visitors could have sneaked all three points in a scrappy second period.
Young midfield trio Morgaro Gomis, David Robertson and Greg Cameron excelled as United dominated the first half.
They passed the ball with great composure on an uneven pitch which is still showing large bare patches.
United did not seem to be missing skipper Barry Robson, who was left on the bench as he sits one booking away from a four-match ban, but all three midfielders had overcome injury fears and they could not maintain their dominance after the break.
Inverness looked stunted in the first period without their star player, Craig Dargo, who was out with a hamstring problem, but they dug in after the interval.
United had their first great chance as early as the fourth minute when Jon Daly just beat Inverness goalkeeper Michael Fraser to a clever through-ball by Christian Kalvenes, 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 Robertson's lob.
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.
Daly then beat Fraser to Dillon's high cross but did not get the direction on his header.
The Irish striker then rose well at the far post to reach a Gomis cross but his header bounced into the arms of Fraser.
The chances kept coming and Hunt sliced wide at the far post after Daly had got his head to another Kalvenes cross.
And the deserved and impressive goal arrived in the 41st minute when Robertson ran in to meet Hunt's cross from the right and looped a header into the far corner.
Inverness came out with more urgency after the interval but the hosts had the first chance when Fraser tipped over McCracken's looping overhead kick.
However, Bayne rose brilliantly in the box to head home Richie Hart's long free-kick.
Daly had a good chance to restore the 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.
Inverness had a decent penalty claim ignored when Kalvenes collided with Bayne in the box before McBain shot wide.
The visitors were looking more likely to score going into the final quarter with nothing sticking up front for United.
Levein was surely tempted to bring on Robson, but he chose Stuart Duff and Craig Conway as United regained the territorial advantage.
Fraser almost dropped Duff's ball across goal and Conway curled a cross just beyond the far post, but neither side really looked like carving out a winner as United stayed a point ahead of Caley Thistle.
Teams:
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).