Kenny Cooper and Darlington Nagbe added goals for the Timbers (10-12-6), who had their eighth shutout of the season.
"Another clean sheet, another home win, and we're in a great position to be in," Cooper said.
Chara's goal came in the ninth minute when he kicked the ball past charging New England goalkeeper Matt Reis.
Cooper scored his fifth goal of the season off a cross from Mike Chabala in the 32nd minute.
Nagbe scored on a header off an assist from Kalif Alhasson in the 65th minute.
The Timbers were the more aggressive team from the beginning, with 13 shots in the first half to New England's seven.
"That was some of the best football I have seen in Major League Soccer this year for 45 minutes," Timbers coach John Spencer said.
In the second half, Portland showcased a fluid, well-balanced defense that held off any attacks.
The victory pushed the Timbers into an eighth-place tie with Houston and Philadelphia in the playoff race, though it could be temporary with the rest of the league's 18 teams in action on Saturday.
Portland is playing in its inaugural season in Major League Soccer.
The Timbers play San Jose at home Wednesday and then have four of their last five matches away from Jeld-Wen Field.
"We're just going to push and hopefully make it to the playoffs," Nagbe said.
New England (5-12-12) has gone winless in eight of nine matches, with the only victory coming last Saturday against FC Dallas.
With just 27 points, the Revolution are tied with Chicago and Toronto FC at the bottom of the Eastern Conference.