Thunder coach Mark Daigneaul gave Gilgeous-Alexander, this season's Most Valuable Player, a break late in the third quarter rather than his usual rest earlier in the fourth.
The Pacers led 101-97 with less than four minutes remaining, but Gilgeous-Alexander scored 13 points and ended the game with 10 free-throws from 10 attempts.
Jalen Williams scored 27 points and made seven rebounds for the Thunder, while Alex Caruso added 20 points off the bench.
Pascal Siakam led the Pacers with 20 points and Tyrese Haliburton 18.
The Thunder host game five at Paycom Center in Oklahoma City at 19:30 local time on Monday (01:30 BST, Tuesday).