Two goals in the space of five first-half minutes from Edward Ofere (38) and Danny Williams (43) gave the home side victory after Robbie Muirhead’s rain-assisted opener in the sodden Highlands (2).
And John Hughes’ side will guarantee a third-placed finish – their highest yet – if they win any one of their remaining three league fixtures, the first of which is away at Dundee on Saturday.
United could yet finish fourth and make the Europa League if Inverness win the Scottish Cup final, but they have won just twice in 15 games and go to St Johnstone at the weekend level on points with their fellow Taysiders.
Saturday’s win over Aberdeen bucked their recent trend of poor results, and match-winner Muirhead was at it again inside two minutes as he capitalised on the awful conditions to put his side in front.
A back-pass held up on the drenched surface, and Inverness keeper Ryan Esson’s desperate clearance fell kindly for Muirhead to find the empty net from distance.
The teenager might have had a half-hour hat-trick, hitting the bar and forcing Esson into a smart stop from a free-kick, but Inverness gradually acclimatised to the conditions and levelled when Marley Watkins fed Ofere at the end of a team move.
Their second was all the work of Williams, who teed himself up for a volley and cracked in left-footed for a third goal this season.
Ofere now has five in 10 Inverness appearances, and he missed a great chance to add a sixth after the break after more good work from Watkins.
United could not make him pay and are yet to beat the Highlanders in three games this season, with a fourth to come at the Tulloch Caledonian Stadium later this month.