Steve Clark made six saves while registering his third shutout of the season for the Timbers (9-10-3, 30 points). Portland has won back-to-back games to move into sole possession of sixth place in the Western Conference.
The Timbers also improved to 3-7-2 on the road.
Houston (3-10-10, 19 points) has dropped six of its last seven matches. The Dynamo are mired in a 16-match winless drought (0-8-8) since beating the Vancouver Whitecaps 2-1 on May 22.
Houston is tied with expansion Austin FC for fewest points in the Western Conference.
Houston held a 19-9 edge in shots. The Dynamo put six on target to Portland's four. Houston goalkeeper Mike Nelson had two saves.
Clark preserved his clean sheet when he deflected a close-range header by Houston's Sam Junqua over the net in the 81st minute.
The Timbers struck in the 15th minute as Mora sent a header in on goal. Nelson made the save, but Chara was there for the rebound and sent a left-footed shot into the net for his third goal of the season.
A short time later, Nelson was called for a foul in the penalty area. Mora stood at the spot in the 20th minute and sent a right-footer into the left corner of the net as Nelson dove in the other direction.
The goal was Mora's team-best ninth of the season.
Houston had a solid opportunity three minutes later, but Fafa Picault sent a header wide right of the net.
Memo Rodriguez took a free kick in the 52nd minute for the Dynamo, but his right-footed blast was stopped by Clark.
Houston's Maximiliano Urruti took a right-footed shot in the 67th minute that went wide left of the net.
Mora narrowly missed a second goal as his right-footed shot went just wide of the left corner in the 78th minute.