Inverness are still looking for their first points of the season after shipping three second half goals.
Sean Dillon's cross was missed by the stooping Barry Robson, but that was enough to put off keeper Michael Fraser and the ball crept into the net.
Stuart McCaffrey then scythed down Mark Kerr from behind and Robson slotted home the spot-kick.
United skipper Robson netted a second penalty on 80 minutes, with Grant Munro guilty of a foul on Lee Wilkie.
Inverness, led by caretaker manager Donald Park, made one change to their team.
Richard Hastings was missing, due to a leg muscle strain, and was replaced by Roy McBain.
Dundee United's Craig Conway was absent due to a foot injury and Willo Flood dropped to the bench, allowing starts for Garry Kenneth and Prince Buaben.
United started with an unorthodox formation as Lee Wilkie, a central defender, was played as a lone striker, with Noel Hunt and Robson offering support from the flanks.
The visitors began in positive fashion and Kerr registered the first shot on target in the 11th minute with a dipping half-volley which was comfortably saved by Fraser.
Inverness then took a grip on the game and United keeper Grzegorz Szamotulski was kept busy.
Ross Tokely's deep cross was flicked into the path of Marius Niculae by Graham Bayne and the Romanian's header produced a brilliant stop from Szamotulski at his near post.
Bayne had a fierce drive beaten away by Szamotulski, before Stuart McCaffrey almost turned in Niculae's brilliant low cross at the back post, only to find the side netting with his lunging shot.
United were struggling to pose the Inverness rearguard any problems, but a Morgaro Gomis shot from 18 yards did have to be tipped wide by Fraser.
The home keeper looked a little foolish after the break when Dillon's speculative cross found the back of the net.
Caley Thistle responded with a Bayne header from Don Cowie's corner which was acrobatically saved by Szamotulski.
However, in the 58th minute the home side fell two goals behind.
McCaffrey fouled Kerr from behind, and Robson coolly placed the ball into the net from 12 yards.
United were in total control and came close when Hunt directed a pass from Wilkie into the path of Robson.
The new Scotland international immediately flashed a shot towards goal, but Fraser was well placed to make a strong parry.
With ten minutes remaining, United were awarded a second spot-kick when Munro's despairing sliding tackle brought down Wilkie.
Robson again took charge of the situation and placed his penalty in exactly the same place as his previous effort.
Inverness CT: Fraser, Tokely, McCaffrey, Munro, McBain, Cowie, Black (Wilson 61), Duncan, Rankin, Bayne (McDonald 75), Niculae. Subs Not Used: Ridgers, Watt, McAllister, Sutherland, Wyness.
Booked: Tokely, McBain.
Dundee Utd: Szamotulski, Wilkie (Robb 85), Dods, Kenneth, Dillon, Kalvenes, Kerr, Gomis, Bauben, Robson, Hunt. Subs Not Used: McLean, Flood, Robertson, Duff, Goodwillie, Cameron.
Booked: Dods.
Goals: Dillon 47, Robson 58 pen, 81 pen.
Att: 4,178
Ref: J Underhil
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