Rolfe smashed a volley into the top of the net for the tying goal in the 70th minute. Fabian Espindola's service from the right flank floated just over the leaping defender Teal Bunbury's head to find Rolfe's right foot.
United coach Ben Olsen praised Espindola's effort as a provider.
"We obviously like when he's scoring goals," Olsen said. "But the times he's able to get in and around the box, and in particular on the end line, it's pretty impressive."
Rolfe then put United ahead from the penalty spot in the 81st minute with a blast into the right corner. It was his first two-goal game as a United player and he needed to convince his teammate for the opportunity.
"I think Fabi (Espindola) expected to get a chance to take it," Rolfe said. "So we just went over there and talked about it. We decided I would take it today, and it worked out."
Miguel Aguilar drew the penalty on Steve Neumann's challenge near the top-left corner of the 18-yard box.
United (9-5-4) ended their two-game losing streak and moved ahead of Seattle and Vancouver to the top of the MLS standings. D.C. also stretched its Eastern Conference lead to seven points over the second-place Revolution (6-5-6), who stayed four points ahead of third-place Orlando.
Charlie Davies gave New England the lead in the 10th minute with a left-footed stab to finish Lee Nguyen's cross. Bunbury flicked it forward to Nguyen who sent a low ball in to Davies near the top of the 6-yard box. It was Davies' seventh goal of the season.
The Revs nearly added another early goal on chance in the 23rd minute when Nguyen found Chris Tierney running up the left side of the area. United goalkeeper Bill Hamid charged out to smother the opportunity and it ultimately proved crucial.
With game-time temperatures in the low 90s, United seemed listless throughout the first half but took the momentum early in the second and Rolfe's first goal seemed an inevitable result.
Revolution coach Jay Heaps blamed the second-half goals on a lack of focus.
"It wasn't like we were under a lot of pressure," he said. "Obviously we weren't good with the ball, and I think that's what frustrates me the most. There was no real pressure and we kept giving the ball back, and I don't know where that comes from and that's a mental lapse."