Rooney scored his eighth goal of the season after the penalty was awarded due to a hand ball in the Revolution box.
Midfielder Juan Agudelo scored in the 61st minute for New England. The Revolution (3-8-4, 13 points) played the last 43 minutes -- 34 regulation, nine stoppage -- with 10 men after keeper Matt Turner took Rooney out.
Mike Lapper served as Revolution interim coach for the third straight game. Recently hired Bruce Arena will take over coaching duties early next week.
New England is 1-0-2 over the three games, allowing just two goals during the stretch after giving up 30 in its first 12 matches.
D.C. (7-4-4, 25 points) moved into first place in the Eastern Conference, one point ahead of the Philadelphia Union, who lost 3-1 to Portland.
D.C. United took 21 shots, with five being on target. Only two of New England's 14 shots were on goal.
Agudelo's goal came five minutes after a red card left the Revolution playing with just 10 men. Midfielder Cristian Penilla had possession on the left flank and he sent the ball into the box to Agudelo, who easily headed it past D.C. goalkeeper Bill Hamid.
New England lost goalkeeper Matt Turner to a red card in the 56th minute when he crashed into Rooney. That left the Revolution playing a man down for the remainder of the contest.
Rooney was chasing a ball toward the box and Turner was initially slow to move forward before closing ground, leaping and aggressively crashing into Rooney, who was attended to for a couple minutes before getting up.
Brad Knighton entered as goalkeeper and his welcome was seeing Rooney line up for a free kick at the top of the box. Rooney sent a blistering right-footed shot on goal and Knighton was up to the challenge and made the stop with his left hand.
New England didn't have a shot on goal in the first half but had a major opportunity in the second minute of the second half.
Cristian Penilla sent a slow-moving pass from the left to the right and defender Brandon Bye approached to unleash a powerful right-footed blast that was stopped by Hamid.