Despite a difficult and disappointing season, D.C. United Coach Ben Olsen has the public backing of General Manager Dave Kasper, who said, “the future is bright with Ben Olsen.” (Ned Dishman/Getty Images)

The instant D.C. United’s­ 13-match winless streak officially ended, with a 3-1 victory over Philadelphia in a U.S. Open Cup fourth-round match before 2,325 at Maryland SoccerPlex, Coach Ben Olsen was arguing a call with the fourth official.

Soon enough, however, the reality hit that the club had won its first game since March 9 and had advanced to a cup quarterfinal, against the New England Revolution on June 26 at SoccerPlex. (United had advanced to the fourth round after winning a penalty kick shootout against Richmond in a match that finished 0-0.)

“We’re finally healthy. It’s a good vibe right now,” Olsen said. “There’s a silent confidence about us that we can get out of this thing. Now is the time.”

United won thanks to three goals from Dwayne De Rosario. Philadelphia entered with the league leaders in goals and assists, both of whom started on Wednesday. Yet it was De Rosario who stole the show.

His opening goal came on a left-footed finish from the top of the box in the 24th minute. To that point, Philadelphia had not taken a shot. His second goal came in the 75th minute, with a right-footed finish from inside the penalty area off an assist from substitute Lionard Pajoy.

After Philadelphia closed to 2-1 on a goal by Jack McInerney — he has a MLS-high 10 in league play — in the 76th minute, De Rosario closed the door.

A defensive miscue on an attempted clear came with goalie Zac MacMath well away from the goal. De Rosario pounced on the loose ball and fired into an empty net from 40 yards.

He was standing right in front of the United bench — and the players on the bench were so certain the 2011 MLS MVP had scored that they began celebrating before the ball crossed the line. As did De Rosario, who entered the night with two goals.

“I’ve known De Ro a long time,” Philadelphia Coach John Hackworth said. “He’s a fantastic player. There’s a reason he was MVP.”

Said De Rosario: “It’s huge. We want to win everything we play and hopefully now we can take this and carry it into our league.”

United also was bolstered by the return of central midfielder John Thorrington; he played his first full game since last season. He had sustained a knee injury in a 1-0 win over Real Salt Lake on March 9. That game marked United’s last victory before Wednesday.

The winless streak had clearly grated on everyone around the team, but perhaps most especially Olsen.

United General Manager Dave Kasper told The Post’s Steve Goff on Tuesday that Olsen’s job is not in jeopardy despite the winless streak.

“Ben gave us a pulse again [when appointed to the full-time job in 2011] and we believe in him and support him,” Kasper told Goff before later adding: “The future is bright with Ben Olsen.”

On Wednesday, the present was bright too. Olsen expressed his intent when, with a 1-0 lead, he substituted a defender for Pajoy, a forward.

In the seconds after the game ended, Olsen received congratulations from Hackworth and from Philadelphia reserve Chris Albright, a longtime friend.

United has a club-record 12-match winless streak in league play, though its next three games are at home against teams with losing records. It starts Saturday night against Toronto FC.

“It’s nice to be continuing in the cup,” Olsen said. “We need to start getting some points now in the regular season, and it starts this weekend with Toronto.”

United notes: Midfielder Chris Pontius, the club leader in assists, left the game at halftime after he sustained the second of two hard fouls in a matter of minutes. Immediately as he came off the field, Pontius was given a quick concussion test before he went to the locker room.

After the game, Olsen said Pontius will go for further tests.

“He told me he didn’t have a concussion. I’m not buying it for a second,” Olsen said. “He didn’t look so hot so we’re going to get all the testing done.” ...

United’s starting lineup featured three former Maryland players — forward Casey Townsend, defender Ethan White and fullback Taylor Kemp. For much of last night’s game there were four former Terrapins on the field as MacMath also played there.