The midfielder came up with the magic on 12 minutes to dump a below-par Tayside team out of Scotland's premier knockout competition.
Inverness should have doubled their lead on the half hour, but Rory McAllister headed over the bar from a swerving Barry Wilson delivery.
More of the passing football was played by Inverness, while Craig Levein's men relied heavily on the height of their players when it came to set-pieces.
United thought they had levelled moments after the interval when David Robertson headed in a cross from Craig Conway, but was ruled offside.
Rare glimpses of a reply came from Collin Samuel and Mark Kerr, but the visitors could not find a way through a strong Highland rearguard.