Houston has now failed to win any of its first 12 games away from home this season, but after an early goal from Ryan Cochrane and some strong play in goal from Revs 'keeper Matt Reis, the team will be pleased with a point.
New England started strong from the opening whistle and Chris Tierney came within inches of giving the home side the lead in the third minute when his free kick struck the crossbar.
But the Revs didn't have to wait long for the opener to arrive as Milton Caraglio's shot was saved on the goal line, only for the ball to fall to the feet of Cochrane, who netted his first goal of the season from a few yards.
However, Houston had the better of the play from there with Kevin Alston clearing a header off the goal line a few minutes later, while Benny Feilhaber did the same for the Revs in the 13th minute.
Reis produced a nice stop on Je-Vaughn Watson's close-range header before Geoff Cameron nodded a ball on goal that forced Reis to tip it over the crossbar.
The second half saw more of the same as Cameron was denied again by Reis from 15 yards, while Weaver's close-range header was kept out by a great reaction save.
Reis looked like he would make the early goal stand up, but as the game approached stoppage time, substitute Carlos Costly headed the ball on target, forcing Reis to make the save but leaving a rebound for Boswell to knock over the goal line from a yard away.
The Revs were hoping to snap a four-game winless streak on Wednesday, but despite the heroics of Reis, they failed to claim all three points.