The Boilermakers (13-5, 4-1 Big Ten) trailed by nine points in the first half and again early in the second before the Illini (9-10, 1-5) went cold. Robbie Hummel, scoreless in the first half, had eight of his 13 points during Purdue's big run, and a basket by Calasan gave the Boilermakers their first lead of the game, 43-42.
A basket by Hummel and six straight points by E'Twaun Moore then helped push Purdue's lead to 51-43 and the Illini never recovered.
A 3-pointer by Trent Meacham pulled Illinois within 58-55 with 5 minutes to go, but Calasan hit three free throws, Grant added two more and then hit a clinching 3-pointer with under 2 minutes remaining.
Grant's 22 points matched the most by any Purdue player all season.
Purdue never led in the first half, missing nine straight shots over the opening 5 1/2 minutes before the initial wave of substitutions helped produce three quick scores by the Boilermakers.
Each of Illinois' first six baskets was by a different player, including consecutive 3-pointers by Chester Frazier and Meacham for a 14-6 lead. Meacham hit his second 3-pointer during a flurry of long-range shots by both teams over the next few minutes, and two straight layups by Pruitt gave the Illini their biggest lead at 21-12.
Purdue came within five points several times before halftime, but Illinois responded each time, including a last-second 3-pointer by Frazier for a 35-27 lead at the break.
Illinois matched that early in the final period at 40-31 before a rebound tip by Hummel, his first basket of the game, started Purdue's comeback.