Al-Farouq Aminu added a season-high 24 points and Evan Turner also had his season best with 22 for Portland, which was without leading scorer Damian Lillard for a fifth straight game.
Kris Dunn scored 22 points and Nikola Mirotic had 18 points off the bench for Chicago, which blew a late lead for a second straight game. The Bulls lost for only the fourth time in 14 games since Mirotic returned to the lineup.
Lauri Markkanen finished with 19 points, including a jumper from the corner that tied it at 120 with 1:14 left in overtime.
McCollum then made his short floater and added a pair of late free throws.
McCollum and Aminu, who made 5-of-6 3-pointers after halftime, carried the Blazers’ offense as they rallied from a seven-point deficit.
After scoring four straight points to tie it at 112, McCollum missed two tries to pull ahead in the final 36 seconds of regulation.