Ian McCall's side notched up their first SPL win of the season over league newcomers Caledonian Thistle.
Caley Thistle took the lead through a second half penalty, converted by Barry Wilson, after Juanjo was fouled in the box.
But United fought back and Chris Innes levelled for the Tannadice side in 71 minutes.
Then Jim McIntryre sealed a 2-1 victory for the Tangerines with a only four minutes remaining.
Grant Brebner was handed his Dundee United debut by boss Ian McCall after arriving from Hibs on Friday.
Thistle boss John Robertson was boosted by the presence of Juanjo whose red card was chalked off by the SFA on Friday following his wrongful dismissal against Celtic last weekend
Robertson also fielded Roy McBain and Richard Hart for Russell Duncan and Steve Hislop, the only two changes to the side which beat Ross County 1-0 in the CIS Insurance Cup in midweek.
Thistle started brightly with their first attempt coming from a 30-yard Hart effort after only two minutes.
Moments later, striker Graham Bayne sent an effort over the woodwrok from outside the box.
In the 26th minute, midfielder Barry Wilson directed a 25 yard drive onto goal but his attempt was well saved by Bullock, who tipped the ball past the post.
United hit back with a chance in the 33rd minute, when Jason Scotland breached the Inverness defence to find Billy Dodds bearing down on goal inside the Caley box.
But the veteran striker tripped over the ball to the amusement of the visiting fans.
Thistle took the lead after the break in controversial fashion when the referee awarded a soft penalty after Juanjo went down in the box.
Barry Wilson stepped up and calmly converted the spot-kick.
With the game sparked into life by the penalty incident, United fought to drag themselves back into the match.
Striker Chris Innes levelled for the Tangerines in 71 minutes, after he was on hand in the box to poke home a rebound from a Billy Dodds strike.
Then with four minutes left, and the home side pressing, Jim McIntyre sent a tremendous left-footed shot past Inverness goalkeeper Mark Brown to give Ian McCall's side three valuable points.
Dundee Utd: Bullock, Wilson, McCracken, Innes, Archibald, McIntyre, Kerr, Brebner, Robson, Scotland, (Grady 78),Dodds (McLaren 83).
Subs Not Used: Hirschfeld, McInnes, Duff, Bell, Kenneth.
Booked: Dodds, Innes.
Goals: Innes 71, McIntyre 86.
Inverness CT: Brown, Tokely, Munro, McCaffrey, Golabek, Hart, Keogh, McBain (Hislop 87), Wilson, Bayne, Juanjo (Prunty 83).
Subs Not Used: Fraser, Dods, Duncan, Thomson, Black.
Goals: Wilson 60 pen.
Att: 6,017
Ref: J Rowbotham (Scotland).