Inverness came from behind to virtually kill off former manager Craig Brewster's slim hopes of leading Dundee United into the Bank of Scotland Premier League's top six.
United full-back Charlie Mulgrew curled home two superb free-kicks and Lee Miller missed a penalty with his side one ahead.
But Caley levelled twice in an even and open first half through Darren Dods and Dennis Wyness before Craig Dargo and Alan Morgan turned their second-half superiority into goals.
Brewster brought in striker Miller for the suspended Barry Robson and pushed Collin Samuel wide left while his Caley boss Charlie Christie kept faith with the 11 who lost on penalties to Partick in the Tennent's Scottish Cup in midweek.
United almost scored after 60 seconds when Mulgrew's long free-kick into the box found David Fernandez in space. He laid the ball inside for Miller but Mark Brown blocked his close-range effort.
Fernandez had a great chance in the third minute when he latched on to Miller's head-on but his lob from 12 yards cleared the crossbar.
Richard Hastings saw a 25-yard shot saved by United goalkeeper Derek Stillie and Dargo headed Richie Hart's cross over moments later.
Another Miller flick-on found Fernandez in the left channel but his powerful effort was parried behind.
Mulgrew opened the scoring in the 18th minute when he curled a 25-yard free-kick from the left channel in off Brown's near post as the goalkeeper awaited a cross.
The on-loan Celtic left-back had won the soft-looking free-kick himself when he went down under a challenge by Hart.
Caley skipper Dods almost doubled United's lead when his header following a Fernandez cross just cleared Brown's far post. Inverness looked shell-shocked and Miller latched on to Grant Brebner's ball over the top but his shot from the right channel was well saved.
Seconds later Miller had an even better chance when United were awarded a penalty after Ross Tokely hacked down Samuel as he ran at the heart of the Caley defence.
Referee Stuart Dougal let the right-back off with a yellow card and the visitors had another reprieve when Miller's low penalty struck the post.
Dods levelled three minutes later on the half-hour mark when he got free of the home defence and headed home Barry Wilson's deep free-kick from the left at the back post.
But Mulgrew curled home another superb free-kick from 25 yards out in the 40th minute.
Again Hart complained about the award when he was penalised for a challenge on Brebner before Mulgrew found the top corner from a central position.
Dargo found space 25 yards out but shot weakly at Stillie and Wyness was foiled by Stuart Duff's challenge, but Wyness levelled in injury time when he slotted home Hart's cutback from the left byline.
The visitors took the lead in the 49th minute when Ian Black slipped Hart clear on the left channel and his ball across the face of goal was bundled home on the line.
Dargo appeared to get the final touch to claim his eighth goal in as many SPL games.
Inverness were working hard to close United down with the home side struggling to maintain any fluency going forward.
United goal hero Mulgrew went off injured to be replaced by Lee Mair, making his first appearance after a year on the sidelines with a knee injury, but his first main contribution was to be booked for a foul on Wilson.
Black came close with a header and Dargo raced onto a through-ball but hit the side-netting after being forced out wide by Stillie.
A flowing move from left to right found Caley substitute David Proctor just inside the United box but Stillie saved his shot across the goal.
United were devoid of ideas and sub Morgan finished the game off with five minutes left with a cool left-foot finish from the edge of the box after Dargo had slipped the ball inside.
Dargo had a 20-yard effort comfortably saved as the visitors held on easily for Christie's first win since being confirmed as boss six games ago.
Teams:
Dundee Utd Stillie, Duff, McCracken, Archibald,Mulgrew (Mair 61), Kerr, Brebner, McInnes (Robertson 78),Fernandez, Samuel, Miller (Goodwillie 78).
Subs Not Used: Samson, Kenneth, Cameron, Gardiner.
Booked: Miller, Mair.
Goals: Mulgrew 18, 40.
Inverness CT Brown, Tokely, Dods, Munro, Hastings,Wilson (Proctor 75), Black, Duncan, Hart (Morgan 79),Wyness (McCaffrey 89), Dargo.
Subs Not Used: Fraser, Golabek, Bayne, Fox.
Booked: Tokely, Hart, Wilson.
Goals: Dods 30, Wyness 45, Dargo 49, Morgan 85.
Att: 6,419
Ref: S Dougal (Scotland).