Gilgeous-Alexander and the Thunder punished an error-strewn performance by San Antonio to claim a victory which leaves the reigning NBA champions 3-2 up with two games remaining in the Western Conference finals.
San Antonio had leveled the series at 2-2 with a battling performance on Sunday but never got going in a lacklustre game five display at Oklahoma City's Paycom Center.
Spurs star Victor Wembanyama had a miserable shooting night, scoring 20 points but making just 4-of-15 attempts from the field while grabbing only six rebounds.
Spurs forward Devin Vassell also had a night to forget, scoring just six points from 2-of-11 shooting after averaging 17 points in the opening four games of the series.
Oklahoma City will head to San Antonio for Thursday's game six with a chance to clinch the series after a typically clinical performance, recovering from a slow start to seal a deserved win.
Gilgeous-Alexander was one of five Thunder players to finish in double figures, with Alex Caruso scoring 22 from the bench including four three-pointers and Jared McCain impressing with 20 points.
Chet Holmgren had 16 points with 11 rebounds, while Isaiah Hartenstein had 12 points with 15 rebounds.
"I might have had the worst start to a basketball game in my career, but the group held it down and kept us in the game," Gilgeous-Alexander said of a sluggish first quarter by the Thunder that saw San Antonio jump into an early eight-point lead.
"Somehow we still won the first quarter but that's a testament to the guys in the locker room.
"I've been saying it all year - we're a group of one through 15, and we wouldn't be this deep in the season without everybody on the team, and it showed again tonight," the two-time NBA Most Valuable Player added.
"We made adjustments after the last game and applied what we learned.
"Against a really good team you've just got to try to be better each and every game, and we definitely got better from the last game."