Basaksehir made a better start to the game and scored in the 20th minute, but that only served to fire up Galatasaray fans and players.
Galatasaray scored twice in the second half, with Sofiane Feghouli and Henry Onyekuru's goals helping the club secure its 22nd Super Lig title.
The two Istanbul sides were locked on 66 points with two matches to play coming into Sunday's showdown.
But as the head-to-head record, rather than goal difference, is the deciding factor in Turkey between teams on equal points, the winner of the derby would win the title.
The two sides had drawn 1-1 in the first half of the season, so Sunday's win meant Galatasaray clinched the title even if they lost the last match of the season next week.
(Reporting by Ece Toksabay; Editing by Mark Potter)
