Colin Clark scored for Houston (10-9-13, 43 points), which extended its unbeaten streak to three games, but missed an opportunity to reclaim first place in the Eastern Conference. The Dynamo are tied with Philadelphia in second a point behind Sporting Kansas City.
Chicago (7-8-16, 37 points) extended its unbeaten streak to four games, but also failed to pick up ground in the playoff race. With three games left, Chicago is seventh in the Eastern Conference and two points behind New York for the final playoff spot.
Clark scored in the 33rd minute off a corner kick, picking up a loose ball left of the net after it had deflected off Jalil Anibaba and slipping it inside the far post.
Oduro tied it up 43rd minute after taking a pass from Baggio Husidic on the upper right box, getting past Bobby Boswell and nailing a right-footed shot into the lower left net.
Bobby Boswell missed a chance to put Houston up in the 13th minute as his header from inside the 6-yard box was saved by Chicago goalkeeper Sean Johnson.
Johnson had five saves, while Houston's Tally Hall had four saves.