Partick edged out Ross County with a stoppage-time winner in a five-goal thriller at Firhill.
County took the lead on 14 minutes when Kevin McKinlay scored from the penalty spot after Gary Irvine was felled.
Thistle levelled through McCulloch's controversial retaken free-kick (33) before Alex Keddie's header (81) put the visitors back in front.
McCulloch scored his second (84) direct from a corner, before Stephen McConalogue scored from six yards.
Partick: Arthur, Sives (Campbell 89), McCulloch, Brady, Boyd, Young (Graham Gibson 59), James Gibson, Donnelly, Keogh, Roberts, Strachan (McConalogue 75). Subs Not Used: Tuffey, Hodge.
Goals: McCulloch 33, 84, McConalogue 90.
Ross County: Samson, Gary Irvine, Keddie, Dowie, McCulloch, Robertson, Gardyn (Gunn 59), Adams, Higgins, Cowie, McKinlay, Gunn (Scott 83). Subs Not Used: Malin, Tiernan, Williams.
Booked: Keddie, Higgins, Gary Irvine.
Goals: McKinlay 14 pen, Keddie 81.
Ref: C Allan.