Defender Ryan Cochrane scored his first goal in nearly four MLS seasons in the 4th minute for New England (4-11-10), now winless in its last five (0-2-3) matches and with just one win over its last 15 (1-8-6).
Houston (7-7-11) has lost only once over its last nine (3-1-5) outings, but is winless this season on the road (0-5-7).
Boswell scored his third goal of the season when Brian Davis sent a corner kick on goal from the left side and Brian Ching unleashed a header at New England goalkeeper Matt Reis. Reis made the save, but in the ensuing scramble, Houston's Jermaine Taylor nudged the ball to the left side where Boswell finished it off.
Cochrane hadn't scored since 2008 with San Josee. After a Benny Feilhaber corner kick out of the left side and his entry pass into the penalty box area, Dynamo goalkeeper Tally Hall and Revolution striker Milton Carnaglio contested for the ball at the right goalpost.
Neither took control and the ball bounced back to the left side, where Cochrane, playing for just the second time in the last five matches, converged on it and pushed it into the net for the go-ahead score.
The Revolution held the one-goal lead into intermission despite Houston having eight shots, five on goal and a half-dozen Davis corner kicks - nearly scoring no less than four times.
Revs defender Kevin Alston (on Bob Boswell in the sixth minute) and midfielder Benny Filthier (on Boswell in the 12th minute) both cleared balls off the goal line for New England.
Meanwhile, Reis made a leaping one-handed save on a header by Je-Vaughn Watson in the 24th minute, tipped a header by Geoff Cameron over the crossbar in the 40th and foiled Adam Moffat twice, in the seventh and again in the 25th.
Reis made a diving save of a drive by Cameron in the 56th minute and a punch save of a header by Cam Weaver in the 63rd.