Gilgeous-Alexander notched five of his side’s season-high 20 three pointers in their 118-104 victory against the visiting Dallas Mavericks in their Western Conference quarter-final.
He also contributed eight rebounds, five assists and three steals, with the Thunder pulling away in the third quarter when they turned a three point half-time advantage into a 90-73 lead.
Klay Thompson and Naji Marshall top scored with 19 points for the Mavericks, while team-mate Luka Doncic was limited to 16 points.
They will play either the Golden State Warriors or the Houston Rockets in the Western Conference semi-final when the competition moves to Las Vegas for the final stages.
In Milwaukee, Antetokounmpo’s exploits helped the Bucks to a hard-fought 114-109 win against the Orlando Magic in their Eastern Conference quarter-final.
Damian Lillard was also key for Milwaukee as he sank a step-back three-pointer to tie the game at 106 apiece with 52.2 seconds left before adding a lay-up and four free throws.
Lillard scored 15 of his 28 points in the fourth quarter and also contributed nine assists.
The Bucks, who will play the Atlanta Hawks or the New York Knicks in the last four, reached the semi-finals of the inaugural in-season NBA Cup last season before being beaten by the Indiana Pacers in Las Vegas.
“We didn’t have the greatest experience there last year,” said Lillard.
“So I think all of us are thinking [about] going back and finishing what we started last year and doing it right this time.”