United had suffered heartache to Celtic in all three domestic competitions in their recent run of matches, and on-loan Hoops midfielder Jackson Irvine was at the heart of the home team’s latest setback.
Irvine scored the opening goal for the Staggies and was involved in Raffaele De Vita’s winner on 72 minutes, with Nadir Ciftci netting from a penalty in between.
United made a positive start and Ciftci fired an early shot narrowly wide, a minute before the striker smashed the ball high into the net from an offside position.
Ciftci was leading the line with authority and County goalkeeper Mark Brown had to be alert to cut out a low delivery from the United striker.
But the visitors took the lead against the run of play when Irvine found enough space in the box to power home a header from a Martin Woods corner on 12 minutes.
United hit back eight minutes later when Aidan Connolly had a shot blocked and went down when challenged by Marcus Fraser as the winger moved to pounce to the rebound.
Ciftci stepped up to take the resulting penalty and sent Brown the wrong way with a confident finish.
The entertainment dipped on a tricky surface, but the match burst into life again after 54 minutes when United survived a big scare after Paul Dixon pulled back Liam Boyce as he latched on to a slack pass at the edge of the penalty area.
Referee Steven McLean awarded the free-kick to the visitors but opted to book the United full-back instead of producing a red card.
Ross County were again thwarted by the officials when Irvine powered a header into the net at another corner, but the effort was not allowed to stand for an infringement on United ‘keeper Radoslaw Cierzniak elsewhere in the box.
Undeterred, County stuck to their task and De Vita pounced to shoot a loose ball back across the ‘keeper after Cierzniak made a brilliant save to keep out another Irvine header.
The result means Jim McIntyre’s side are 10 points clear of bottom team St Mirren, and just four points behind Partick Thistle in ninth place.