The victory extended the Impact's winning streak to five games and moved the club to within a point of the fifth-place United for the final playoff spot in the Eastern Conference.
''Over the last month or so, we've been very good and we've worked hard. We've earned the success we've got right now,'' Impact captain Davy Arnaud said.
D.C., which hasn't won back-to-back games since late May, has three games in hand.
Marco Di Vaio also scored for Montreal (12-13-3).
United fell to 12-9-4 on the season.
Leading 1-0 at halftime, Bernier converted a penalty kick in the 50th minute for his eighth goal of the season.
With the goal, he became the first player since Jamie Moreno in 2009 to score six goals on penalty kicks in a season.
It was also the Impact's ninth penalty kick goal in as many attempts this season.
''I've never seen a season like this where one team has had so many penalty kicks. As long as we're winning, I'm happy,'' Bernier said.
Playing its third game in seven days, Washington was dealing with fatigue. But coach Ben Olsen was pleased with his team, in spite of the rough schedule.
''I was very happy with the effort and the mentality from the group. You don't get a break,'' he said. ''It's tough on two days' rest.''
Montreal had chances to add to its lead in the second half, including several from Di Vaio. The Impact forward got a perfect setup from Bernier in the 63rd minute, but the ball sailed over the net. Di Vaio had another chance for his second of the match in the 81st minute, but his shot went wide.
Montreal goalkeeper Troy Perkins preserved his team's two-goal lead in the 78th minute with a diving save to deny D.C. midfielder Marcelo Saragosa.
Bernier then added his second goal of the game in injury time on a slick finish past United goalkeeper Bill Hamid.
Di Vaio was caught offside several times early in the first half, but got his chance in the 24th minute when Bernier found him behind the D.C. defense. He outwaited Bill Hamid and beat him to the far corner for his third of the season.
- Patrice Bernier
- Montreal Impact
- Marco Di Vaio