Eric Brunner scored the only goal of the match in the 44th minute when he headed home Mike Chabala's corner from the top of the six-yard box at the front post but there were plenty of opportunities for both sides to score throughout the contest.
Chivas' Frenchman Laurent Courtois' sizzled long range attempt was tipped over the crossbar by Troy Perkins in the 18th minute before Goats goalkeeper Dan Kennedy denied David Horst's pointblank header with a tremendous diving save just after the half-hour mark.
Timbers gloveman Perkins tipped another one over when Simon Elliott shot on target from a long free-kick on the stroke of half-time and then Kennedy made another big save to deny Kalif Alhassan in the 62nd minute.
Chivas had a great chance to tie up the match in injury time when Justin Braun's header across goal was missed by Courtois who tried a volley on the outside of his left foot when perhaps the inside of his right could have landed the visitors a point.
Portland moved up to sixth place on the Western Conference table, overtaking Chivas who dropped to seventh following their third match without a win.