John Rankin's long-range strike put Peter Houston's side in control at half-time and Scott Robertson and Johnny Russell added goals after the break.
United - sixth going into the game - have now leapfrogged Hearts and St Johnstone as they chase a European place. Inverness manager Terry Butcher will be disappointed at his side's finishing as their hopes of a top-six finish were damaged.
Dundee United boss Houston made just one change to the side that beat Hearts 2-0 at Tynecastle last weekend as Paul Dixon returned from suspension and replaced Barry Douglas at left-back.
Butcher tinkered with his line-up following a crushing 4-1 home defeat to Rangers in their last outing.
He made three changes, with Roman Golobart, Ross Tokely and Shane Sutherland replacing Steve Williams, Graeme Shinnie and Jonny Hayes.
United made the early running and Gary Mackay-Steven had a penalty claim turned away by referee Alan Muir after his cross struck Josh Meekings on the hand.
From the resultant corner, Gavin Gunning's attempted shot found Robertson and he headed over from six yards.
Caley responded briefly but United took the lead in the 14th minute with a wonder strike from Rankin. Inverness captain Richie Foran could not control a poor clearance from goalkeeper Ryan Esson and Rankin won the challenge, stepped forward and sent a dipping 25-yard drive into the top corner.
United deserved their lead but Inverness almost equalised instantly when Gregory Tade spun in the box and picked out Billy McKay. The striker managed to poke a shot towards the corner but United goalkeeper Dusan Pernis raced from his goal to make a brave block.
Tade blazed a 20-yard drive wide as Caley chased an equaliser while United midfielder Willo Flood tried his luck from a similar distance but his shot soared over the bar.
The game lost its flow as half-time neared and Inverness defender Golobart was booked for clattering into Russell.
United captain Daly - well marshalled by the visitors - then finally broke free but could not divert Dixon's raking pass on target.
Daly was involved again in the 40th minute when he slipped a pass to Russell, but Esson pulled off a fine low save to deny him.
United started the second half on top and Dixon twice picked out Daly with crosses, but the big striker could not convert.
The home side were out to kill the game and Robertson grabbed the second goal in the 52nd minute.
Foran was booked for a tug on Russell and Flood's free-kick found Daly at the back post. He climbed above Tokely and headed across goal for Robertson to head in from six yards.
Inverness faced an uphill battle but Nick Ross almost connected with Sutherland's free-kick at the back post.
United had another penalty claim turned down when Golobart blocked Russell's header with his hands. Caley were living dangerously and Esson survived a big scare when he dropped Robbie Neilson's long throw and Daly fired over the bar..
McKay fired over from 12 yards as Caley wasted a chance to get back into the game in the 70th minute. Substitute Claude Gnakpa also fluffed a good opportunity after creating space in the box.
United then killed the game off in the 78th minute with a moment of magic from Russell. Daly picked him out in the box and the Scotland Under-21 star danced past three challenges and found the bottom corner.