Ryan Smith set up the 17th-minute score when he darted through the left side, beating a pair of defenders, and sent the ball toward the net, where Timbers goalkeeper Troy Perkins dove to slow it down.
Perkins couldn't stop it completely and the ball came to Bolanos, who shook off Kosuke Kimura and put in into the net for his first MLS goal.
The Goats (6-7-5) notched the win after sustaining a 4-1 loss to Seattle in their previous match.
Portland (5-10-4) never mounted much of a threat to Chivas goalkeeper Dan Kennedy.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys