John Daly headed the visitors ahead just after the break before Craig Conway rifled home a quickfire second.
David Robertson headed home the third from a Conway corner before Adam Rooney netted what turned out to be a mere consolation.
Jamie Duff replaced suspended defender Ross Tokely for Inverness as they looked for their second home win of the season on a cold day at the Caledonian Stadium.
Striker Andy Barrowman also started, with youngster Garry Wood dropping to the bench.
United boss Craig Levein elected to replace injured forward Francisco Sandaza with Conway, while midfielder David Robertson came in for the suspended Willo Flood.
United put the Inverness goal under pressure straight from the first whistle.
Daly's deflected header went inches wide of Ryan Esson's goal after four minutes before Garry Kenneth's header rolled agonisingly across the face with no attacker able to steer the ball into the net.
Iain Vigurs had a chance to test Lukasz Zaluska after 11 minutes but the young midfielder dragged his shot wide from 25 yards.
Barrowman then saw his clever first-time effort from a Richard Hastings cross hit the side-netting as the home side began to stretch the United rearguard.
Don Cowie was next to break through a static United back four but the midfielder's lobbed effort landed the wrong side of the crossbar.
A fantastic ball from Kenneth gave Daly a chance to test Esson but the Irishman's volley sailed over the bar.
David Proctor received the first booking of the day for a late challenge on Conway and Danny Swanson and Michael Kovacevic followed him into referee Brian Winter's notebook soon after.
The home side were growing in confidence, with an Ian Black shot taking a deflection before finishing wide of Zaluska's post.
Both sides struggled to create much up front, with neither goalkeeper really having a save to make as the first half drew to a close.
Daly headed United into the lead five minutes after the break when the powerful Irishman was quickest to react to Swanson's inviting cross.
Esson watched helplessly as the ball sailed into the top corner to give Daly his fifth league goal of the season and eighth overall.
Black was fortunate to avoid being cautioned after a string of late challenges in quick succession, with the fiery midfielder doing his utmost to get Inverness back in the game.
Craig Brewster brought on a second striker after 63 minutes, with Rooney replacing Dougie Imrie.
However, it was the visitors who doubled their lead two minutes later.
Daly headed Scott Robertson's cross into the path of Conway, who managed to turn in the box before rifling the ball past Esson, much to the delight of the vocal travelling support.
Barrowman could have given his side a lifeline but the former Ross County man sliced his effort wide.
David Robertson headed Levein's side into a commanding lead after 71 minutes when he managed to get on the end of a Conway corner in a packed penalty box.
Substitute Rooney grabbed a goal back for the home side less than two minutes later when he volleyed home a driven cross from Cowie.
With less than 10 minutes remaining, Swanson could have given United a fourth but his curling free-kick deflected off the Caley wall and went inches over Esson's crossbar.
Inverness brought on youngsters Wood and Zander Sutherland for Barrowman and Vigurs.
Swanson had a second attempt on goal from a free-kick on the edge of the area after Conway had been brought down by Duff but the United playmaker again fired over.