After a cagey start from both sides, Inverness fashioned the game's first real chance and it almost resulted in a goal on his home debut for Marius Niculae.
A marauding run down the right by Ross Tokely found the head of Graham Bayne at the back post who directed it into the path of the Romanian, but his neat flick produced a wonderful reaction stop from Dundee United stopper Grzegorz Szamotulski.
The Polish goalkeeper was soon called into action again as a long, hopeful ball found Bayne racing in on goal, only for his volley from the angle of the box to be parried away for a corner.
Caley Thistle were now cranking up the pressure and from the resultant corner, Niculae picked up the ball at the back post and drilled the ball across the face of goal, but a stretching Stuart McCaffrey could not turn the ball into the unguarded net from less than five yards.
With central defender Lee Wilkie deployed as a makeshift striker, Dundee United struggled to create anything of note in the final third, although Garry Kenneth should perhaps have done better than head the ball across goal from Barry Robson's free-kick.
The visitors, however, improved vastly attacking-wise after the break, although it was through some good fortune that they took the lead two minutes into the second half, Sean Dillon's cross from the right evading everyone before nestling in the corner of the net.
Slowly but surely, United began to gain the upper hand and after Mark Kerr tumbled inside the box under a challenge from both McCaffrey and Rankin, referee John Underhill pointed to the spot.
Former Caley Thistle player Robson took responsibility for the spot-kick and calmly sent Michael Fraser the wrong way to make it 2-0 to the Arabs with just over half an hour remaining.
A Niculae strike from long range was about all Caley Thistle could muster in a poor second half and the home team's misery was compounded nine minutes from time when Robson scored an almost identical penalty to his first, after Grant Munro was adjudged to have brought down Wilkie.