Trailing 2-0 midway through the second half, the Fire got the board in the 68th minute when midfielder Alex found Magee through traffic in the box with a through-ball, which he converted for an easy score.
Chicago (3-7-3) got the equalizer 14 minutes later when Paladini sent Magee's free kick into the net.
Diego Valeri and Ben Zemanski each scored for the Timbers (5-1-8), who stretched their unbeaten streak to 12 games.
2014: NFL Cheerleaders [PHOTOS]
LeBron James reveals his new Nike shoes