Jon Daly nodded home towards the end of an entertaining first half at Tannadice and Lee Wilkie made some steady pressure count in the 65th minute with another header.
Inverness missed some first-half chances but rarely looked like launching a comeback, even after Wilkie's last-minute own goal.
The visitors, who had won their previous two matches, started brightly and the recalled Don Cowie volleyed wide from a tight angle after Michael Fraser's huge kick-out.
United twice threatened from Craig Conway set-pieces in quick succession around the 15-minute mark.
Wilkie volleyed over the stand after Scott Robertson had headed on a free-kick before Fraser clawed Daly's header off his line following a corner.
In between, referee Iain Brines turned away strong appeals for a penalty as United claimed Willo Flood's cross was handled by Richard Hastings.
Inverness were looking sharp going forward and Andy Barrowman just failed to make contact with Cowie's teasing ball across the face of goal.
Barrowman then beat Wilkie to a through ball and stayed on his feet despite appearing to be clipped by the defender.
However, he was closed down by goalkeeper Lukasz Zaluska and Wilkie, with Brines waving him away as the striker made his case for a penalty.
Francisco Sandaza's hesitancy lost him a shooting chance following a slick one-two with Daly.
Inverness spurned an even better opportunity on the half-hour mark as they broke purposefully in numbers.
Cowie rolled the ball inside from the left but the unmarked Roy McBain dragged his shot wide from 12 yards.
United almost made them pay moments later but Jamie Duff headed off the line after Darren Dods had met Conway's corner 10 yards out.
The home side broke the deadlock following a good spell of possession in the 40th minute when Daly powerfully headed Sean Dillon's right-wing cross into the bottom corner of the net from 12 yards.
Inverness brought on Barry Wilson for the injured Ian Black and they almost suffered another blow within two minutes of the restart, when Sandaza headed Conway's cross inches past the far post.
Hastings got a header on target after a good passing move but Zaluska easily saved and United were looking more dangerous.
Fraser parried Flood's 25-yard drive after a good break from left-back Paul Dixon and Daly headed just wide from Conway's brilliant cross.
United continued to push Caley Thistle back and Wilkie headed in off the bar after fellow centre-back Dods had nodded Dixon's centre back across the six-yard box.
Substitute Roy O'Donovan was inches away from a third two minutes later when he stabbed Morgaro Gomis' cross just past the far post.
Inverness boss Craig Brewster brought on striker Adam Rooney for midfielder McBain and suddenly the hosts found themselves under pressure.
Zaluska pushed away Wilson's excellent curling effort towards the far corner before the veteran crossed for Barrowman to head off the post.
Rooney nodded home seconds later after Ross Tokely mis-hit a shot but the Irishman was correctly ruled offside.
Zaluska then got down well to hold Dougie Imrie's powerful long-range drive, but United soon regained control and substitute Danny Swanson's 30-yard strike was parried over by Fraser.
Wilson's last-minute corner found the net via Wilkie's thigh but Inverness could not get the ball in injury-time.