A late Bob McHugh goal ensured Morton secured all three points against the Championship title favourites.
With the game approaching the final ten minutes, substitute Denny Johnstone knocked the ball down to McHugh who fired an unstoppable half-volley high beyond Scott Fox.
Ross County began the day top of the table and they took a deserved lead on 58 minutes through Don Cowie. Iain Vigurs, majestic throughout, played a glorious pass and the former Scotland internationalist raced clear and toe-poked beyond Ryan Scully.
Michael Tidser scored a brilliant equaliser minutes later, unleashing a venomous left-footed strike that arrowed past Fox.
While the points stayed in Greenock, the visitors will be ruing numerous missed opportunities, with Ross Draper the main culprit.
He should have opened the scoring on 15 minutes but could only hit the bar with a diving header and just after the break he failed to connect properly with Sean Kelly’s brilliant free kick.