Lucas Dulle drew the assist on the winner as the Cubs improved to 4-1-0 on the season, good for first place in the Gary Wournell South Division.
Medicine Hat spent much of the night killing penalties, taking 30 minutes in infractions to Strathmore's 26, and went scoreless on four power-play chances while the Kings converted once in six opportunities.
Strathmore opened the scoring on a short-handed goal by Luke Nottveit at 16:04 of the first period, his second of the season. The Cubs were held off the board in the opening frame despite sending 15 shots at Kings goaltender Connor White.
Josiah Jackson tied it unassisted at 15:43 of the second period for his first goal of the season. Jackson then received a 10-minute misconduct at the same stoppage; Strathmore's Keaton Kish was also handed a misconduct on the play.
Brodie Heimbecker put Medicine Hat ahead 2-1 just 2:41 into the third, assisted by Randen Collier and Jackson Brassard. Heimbecker's goal was his fifth of the year. The Kings pulled even at 5:47 when Adam Moore scored on the power play, his second of the season, with Emery Medicine Shield picking up the assist.
Cubs goaltender Kayden Van Ham made 31 saves on 33 shots to earn the win. White stopped 34 of 37 shots in taking the overtime loss.
Medicine Hat heads back out on the road next Saturday when the Cubs visit the Rimbey Royals at 8:30 p.m. at the Vern Poffenroth Memorial Arena in Rimbey.