Gilgeous-Alexander, the reigning NBA Most Valuable Player and a finalist for this year's MVP, connected on 15-of-18 shots from the floor on the way to a career-playoff high.
"(I was) just trying to let the game come to me, use my teammates out there as weapons," Gilgeous-Alexander told broadcaster NBC after the defending champion Thunder moved within one win of advancing to the Western Conference semi-finals.
"I know they're going to try to make it tough on me, make me play in the crowd," added Gilgeous-Alexander, who made 11-of-12 free throw attempts. "The guys did a great job of just playing outside of that tonight ... we looked pretty good out there."
Gilgeous-Alexander made his first nine shots before his first miss midway through the third quarter. He corralled the rebound from that missed three-pointer and stepped in to make a mid-range jumper.
Dillon Brooks scored 33 points for the Suns, who grabbed an early nine-point lead and kept it close in the second quarter but couldn't find a way to stop Gilgeous-Alexander down the stretch.
"We just stuck with it," Gilgeous-Alexander said. "We did a good job of just staying true to who we are through the adversity, through the crowd, through a really good team on the road."
Ajay Mitchell scored 15 points, and Alex Caruso added 13 off the bench for the Thunder, who are trying to become the first repeat champions since Golden State in 2017 and 2018.
They'll try to polish off a sweep in the best-of-seven series on Monday in Phoenix, where the Suns will be painfully aware that no NBA team has rallied from 0-3 down to win a playoff series.