Galchenyuk scored the winner on a penalty shot late in the second period for the Sting (6-6-1), who snapped a three-game slide.
Alex Basso returned to the lineup after serving a three-game suspension for Sarnia and scored his first of the season, while rookie Bryan Moore added the first goal of his OHL career.
Nick Latta rounded out the scoring for the Sting, while Reid Boucher chipped in with two assists.
Elsewhere in the OHL it was: Barrie 2, Brampton 1 (OT); Niagara 5, Sault Ste. Marie 1; and London 5, Peterborough 4 (OT).
At Sarnia, Ont., Jordan Maletta and Josh Ho-Sang scored for the Spitfires (6-5-3), who let leads of 1-0 and 2-1 slip away.
Jaroslav Pavelka stopped 40 shots in taking the loss.
The Sting finished the night 1-4 on the power- play, while Windsor was 0-for-5.
Sarnia forward Nikolay Goldobin saw his seven-game point streak come to an end.
Colts 2, Battalion 1 (OT)
At Barrie, Ont., Aaron Ekblad scored on the power play at 4:33 of overtime as the Colts (10-3-1) edged Brampton (5-4-5).
IceDogs 5, Greyhounds 1
At St. Catharines, Ont., Brock Beukeboom had three assists as Niagara (9-4-1) pounded Sault Ste. Marie (7-7-0).
Knights 5, Petes 4 (OT)
At Peterborough, Ont., Scott Harrington scored on the power play with 32 seconds left in regulation as London (8-3-1) came back to down the Petes (2-7-3).