The 19-year-old powered Andy Rose’s dangerous cross into the top corner under little pressure hours after signing on loan from Stoke.
The goal came right at the end of a poor first half and Motherwell drilled home their advantage when Curtis Main netted his first goal for the club just after the restart.
The Lanarkshire club had become something of an internet phenomenon this week with their pastiche of Manchester United’s Alexis Sanchez video attracting several million views on social media.
But the piano-playing star of the viral video, Peter Hartley, was suspended after making his loan move from Blackpool a permanent transfer and they got back to the more serious business of recording their first Ladbrokes Premiership win since November 18 to move back into the top six.
County started with Souttar and fellow new signing David Ngog on the bench but the defender only had to wait six minutes for his debut after skipper Andrew Davies limped off.
The former Dundee United player and his new team-mates largely kept Motherwell at bay until his faux pas, although Nadir Ciftci had come close with a deflected strike and Craig Tanner’s free-kick dipped just too late.
County rarely threatened but Inih Effiong was not far away with a shot on the turn.
Motherwell had a penalty appeal rejected when Chris Cadden’s cross appeared to hit Michael Gardyne’s hand moments before Souttar’s intervention.
County then found themselves two down inside two minutes of the restart as Motherwell’s new strike pairing combined to good effect. Ciftci robbed Kenny van der Weg on the right wing and delivered a teasing low cross which Main dinked first time over Aaron McCarey.
County soon brought on former Liverpool striker Ngog and they started testing the Motherwell defence around the hour mark.
Ross Draper twice threatened with headers but was denied by a reaction stop by Trevor Carson and a goal-line clearance from Main.
Motherwell threatened sporadically on the break and some Tanner free-kicks caused anxiety among the visitors and they were relatively comfortable at the back as the game progressed.
Ngog had a sight of goal but sliced wide from 18 yards as bottom club County remained without a victory since beating Motherwell on November 4.