Craig Curran nodded home from close range after 33 minutes to chalk up a fourth consecutive win for County, who move three points clear of bottom club St Mirren.
Shortly before the hour, Thistle had Kallum Higginbotham sent off for a rash challenge on Michael Gardyne.
Motherwell are a point above St Mirren after Scott McDonald's free-kick sealed a 1-1 draw with Kilmarnock at Fir Park.
Kilmarnock's top scorer Tope Obadeyi rifled in the opener after 20 minutes but the visitors were reduced to 10 men on the stroke of half-time when Darryl Westlake collected a second booking.
McDonald curled in superbly from the resultant set-piece but Motherwell were unable to force back-to-back wins for the first time since December.
Get the best features, fun and footballing frolics straight to your inbox every week.