McCamey, a freshman guard, made 9 of 14 field goals and all six of his 3-point shots.
Shaun Pruitt added 14 points and nine rebounds for the 10th-seeded Fighting Illini, who advanced to play either No. 22 Indiana or Minnesota in the semifinals on Saturday.
E'Twaun Moore scored 22 points and Robbie Hummel added 10 points and 12 rebounds for second-seeded Purdue.
The Illini advanced to the semifinals for the 10th time in 11 Big Ten tournaments. Purdue, which had its highest seed ever, won 12 of 13 before the loss. The Boilermakers beat the Illini twice in the regular season.
Illinois led 67-66 in overtime when Mike Davis got a perfect pass from McCamey and scored on a backdoor cut to make it 69-66. On Illinois' next possession, Davis rebounded McCamey's miss and scored on an acrobatic putback to make it 71-66 with a minute left.
Purdue didn't make another field goal. The Boilermakers missed their last 12 shots.
Purdue (24-8) led 60-58 late in the second half when Chris Kramer scored on a drive and converted a 3-point play to put the Boilermakers up 63-58 with 1:12 to play.
Pruitt scored and was fouled by Hummel at the other end with 45 seconds left, but he missed the free throw and Hummel rebounded with Purdue ahead 63-60.
Kramer traveled with 31 seconds left to give Illinois (15-18) a chance to tie, and McCamey made a 3-pointer over Kramer, the Big Ten defensive player of the year, with 18 seconds to play. Kramer missed a mid-range jumper as time expired, and the game went to overtime.
Illinois led 13-8 in the early going before Purdue went on a 15-0 run in 5 1/2 minutes to take a 23-13 lead. Illinois fought back, and Pruitt scored on a tip-in with 3.6 seconds left to tie the score at 28 at halftime.
The Illini shot 50 percent in the first half, but had 11 turnovers.
