Ihemelu scored off Dax McCarty's free kick to help FC Dallas improve to 1-1-4. McCarty's kick from about 30 yards out on the right was headed by Brek Shea from the left post to Ihemelu, who headed it in just inside the far post.
FC Dallas went down a man in the 72nd minute when Jair Benitez received a straight red card and ejection for elbowing Houston striker Luis Landin in the face.
Houston (3-3-1) had an opportunity to tie it in the 87th minute when Danny Cruz gave Brad Davis a point-blank shot in front of the left net, but it was saved by Kevin Hartman, who made three saves.
The win was FC Dallas' first in Houston. Dallas is 1-5-2 in MLS regular-season games in Houston and 1-7-2 in all competitions.
National team forward Brian Ching, hoping to recover from a hamstring injury in time to make the U.S. World Cup squad, did not dress.