Inverness twice came from behind to take the points after a sensational match at Tannadice.
Charlie Mulgrew put United ahead with a curling free-kick from 25 yards, before Lee Miller hit the post from the spot.
Darren Dodds headed in the equaliser but Mulgrew had other ideas and curled home another glorious free-kick.
Dennis Wyness levelled the scores at the break, with Craig Dargo stabbing Inverness in front after the restart. Alan Morgan then made the points safe.
United manager Craig Brewster was facing his former team for the first time as he sought to push his side up the table.
The home side almost scored after 60 seconds when Mulgrew's long free-kick into the box found David Fernandez in space.
Caley come back to haunt Brewster
He laid the ball inside for Miller but Mark Brown blocked his close-range effort.
Richard Hastings saw a 25-yard shot saved by United goalkeeper Derek Stillie and Dargo headed Richie Hart's cross over moments later.
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 clearing header grazed the far post.
Inverness looked shell-shocked and Miller latched on to Grant Brebner's ball over the top but his shot was well saved.
Seconds later, Miller had an even better chance when United were awarded a penalty after Ross Tokely hacked down Colin Samuel.
Christie delighted with victory
However, the visitors had another reprieve when Miller's low penalty struck the post.
Dods then levelled the scores shortly after when he got free of the home defence and headed in Barry Wilson's deep free-kick.
But Mulgrew curled home another superb free-kick from 25 yards out in the 40th minute.
Wyness pulled the visitors level once again when he slotted home Hart's cutback from the left byline.
The jags took the lead for the first time after the interval, 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.
Five minutes before time, substitute Morgan finished the game off with a cool left-foot finish from the edge of the box.
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