Marco Di Vaio also scored for Montreal (12-13-3).
D.C., which hasn't won back-to-back games since late May, has three games in hand. United fell to 12-9-4 on the season.
Bernier converted a penalty kick in the 50th minute for his eighth goal of the season and a 2-0 lead.
With the goal, he became the first player since Jamie Moreno in 2009 to score six goals on penalty kicks in a season. Bernier added his second goal in injury time on a slick finish past goalkeeper Bill Hamid.
In other league action, Federico Higuaín and Jairo Obando Arrieta each scored twice to lead the host Columbus Crew to a 4-3 win over the New England Revolution.
Robin van Persie scored his first Manchester United goal in a 3-2 victory over Fulham, as Chelsea made it three straight wins to start the English Premier League season.
Shinji Kagawa and Rafael da Silva also scored at Old Trafford as United rebounded from last week's season-opening loss at Everton. Chelsea beat Newcastle, 2-0; Swansea beat West Ham, 3-0; and Everton defeated Aston Villa, 3-1.
Wigan won, 2-0, at Southampton; West Brom snatched a last-second 1-1 tie at Tottenham; Norwich and QPR drew, 1-1; and the Sunderland-Reading game was postponed by a wet field.
Rooney hurt, out 4 weeks
Manchester United manager Alex Ferguson said Wayne Rooney could be out for a month after sustaining a deep gash to his right leg in Saturday's 3-2 win against Fulham.
Rooney was carried off the field on a stretcher in injury time after getting caught by Hugo Rodallega.
"He's got a bad one. He's gone to hospital," Ferguson said. "It looks as he'll be out for maybe four weeks."
The injury is likely to keep Rooney out of England's first two World Cup qualifiers, against Moldova on Sept. 7 and Ukraine on Sept. 11.
He will also likely miss the beginning of United's Champions League campaign and potentially the Sept. 23 away game against Premier League rival Liverpool.