Cam Weaver helped set up the goal when he headed Brad Davis' corner kick off the crossbar, and the ball went straight up. Freeman cleared room in a pack of Revolution players and tapped it in.
Freeman's score came after Bobby Boswell's shot went through a group of New England players and appeared to go over the endline, but Zack Schilawski cleared it away, and it was not called a goal.
Houston (2-1-2) also extended its unbeaten streak to four games.
Matt Reis made seven saves for New England (1-2-3), which has lost two straight and is winless in its last four.