The Boilermakers had a chance to extend a 76-75 lead in the closing seconds but Kendall Stephens missed the front end of a 1-and-1.
That allowed Robinson to corral an inbounds pass in the far corner with 2.9 seconds left and connect on a baseline runner for the game-winner.
He finished with 17 points and Nik Stauskas netted 15 as the Big Ten Conference-leading Wolverines (20-7, 12-3 Big Ten) notched a third win in four games.
Caris LeVert put in 14 points and Jordan Morgan provided 13 with 10 rebounds.
Purdue (15-13, 5-10) was paced by Terone Johnson with 24 points and brother Ronnie with 21.