United forward Wayne Rooney beats Real Salt Lake goalkeeper Nick Rimando for a first-half goal, the second of his three on the night in D.C.'s 5-0 win. (Geoff Burke/USA Today Sports)

First and foremost, D.C. United signed Wayne Rooney to score goals. The MLS organization appreciates his leadership and experience, the ravenous work ethic and his cunning with the soccer ball at his glorious feet.

But the fans have come to Audi Field since last summer to watch the former Manchester United ace to change matches with his scoring touch, whether on penalty kicks, free kicks or sterling kicks from a variety of angles and distances.

Rooney, 33, proved his value over a partial season last year, and on a cold Saturday night, he opened his 2019 scoring account with his first hat trick, plus an assist, during a 5-0 demolition of Real Salt Lake.

Scoreless in the first two matches, Rooney converted a penalty kick in the 34th minute and converted from close range seven minutes later. After the visitors received the first of their two red cards, he added his third goal at the end of a breathtaking team buildup. Later, he served a corner kick to Lucas Rodriguez for a wicked volley from the top of the box.

“To score a hat trick is always great,” said Rooney, the English national team’s all-time scoring leader. “I am really pleased with getting the three goals and I am pleased for the team. It was a great victory for us.”

United (2-0-1) extended its regular season unbeaten streak to 13 and spoiled the last match in Washington for Real Salt Lake goalkeeper Nick Rimando, a former D.C. star who, in his 20th and final season, was honored in a pregame ceremony.

The first red card, just before halftime, all but killed the suspense, and the second ejection, midway through the second half, opened the floodgates. United was elegant in the attack, tidy in defense and ruthless when the situation called for it.

And Rooney continued to show he is far from finished.

“He has been doubted for the last three years, and he continues to do what he does,” D.C. Coach Ben Olsen said. “He’s done it since he was 16. He has scored goals and played at a high level. I don’t know why that would change.”

Rooney received a bounty of assistance. Defensive midfielder Junior Moreno (two assists) was immaculate in his tackling and distribution, Luciano Acosta danced past defenders, and the back line shielded goalkeeper Bill Hamid, who has yet to concede a goal this season.

“Chemistry is on another level,” Hamid said. “We went about things in the right way. We didn’t lose our heads [in the physical match]. We stayed calm, and it paid off.”

Olsen retained the same starting lineup from the first two matches, a victory against defending champion Atlanta and a draw at New York City FC.

United took some time to find its rhythm, but once it did, Real Salt Lake was chasing shadows. It began with Rooney’s penalty kick past Rimando, who has excelled in his career at stopping the 12-yard attempts. Rimando went one way, Rooney the other.

What led to the penalty kick, however, was debated. A step inside the penalty area, Marcelo Silva stepped on Paul Arriola’s right ankle just after the D.C. winger had released the ball. Referee David Gantar did not whistle a foul, but while Arriola received treatment, he checked video replay and awarded the penalty.

Seven minutes later, United’s high pressure yielded the second goal. Leonardo Jara bore down on Aaron Herrera, whose heavy touch relinquished the ball to D.C.'s right back.

Before Real Salt Lake (1-1-1) could regain its shape, Jara supplied the unmarked Rooney in the box. As Rimando charged, Rooney coolly chipped the ball into the net.

Real Salt Lake’s problems deepened during stoppage time when Jefferson Savarino’s raised foot caught Acosta in the face, prompting Gantar’s red card.

“Maybe a little harsh there,” Olsen said.

On the ensuing free kick, from almost at the sideline, Rooney’s bid for a first-half hat trick skipped off the top of the crossbar.

Down a player and down two goals, Real Salt Lake tried to force the issue in the second half. United, however, absorbed mild pressure and threatened to put the match away.

Rooney should have done the honors in the 54th minute, but with Rimando at his mercy, the close-range header veered wide.

“If I don’t get another chance,” Rooney said, “I would’ve been really disappointed. It was almost too easy.”

He made no such mistakes in the 65th, capping a gorgeous sequence.

Moreno won the ball in midfield and fed Acosta, who drew attention centrally and returned it to Moreno rushing the left flank. Moreno’s cross connected with Rooney for a sliding redirect from close range.

Two minutes later, Real Salt Lake had another player dismissed after Silva knocked down the surging Rodriguez from behind just before entering the penalty area. It was Silva’s second yellow card.

Rodriguez’s tally in the 76th minute was a rasping volley, struck with perfect technique, for his first MLS goal. “I couldn’t believe it actually went in,” he said. “The best goal of my professional career.”

Ulises Segura, a second-half sub, put away Moreno’s pass in the 80th.

“It was a mature second half in the way we went about it,” Olsen said. “The tempo was right, and obviously we finished off a few plays.”

Notes: United is off next weekend and will visit Orlando City on March 31. ...

Moreno (Venezuela) and Arriola (United States) will report for international duty this week. Chris Durkin will join the U.S. under-20 squad in Spain for two friendlies as part of preparations for the U-20 World Cup this summer in Poland. All three will return for the Orlando trip. ...

Aston Villa and Bordeaux are among the clubs under consideration for a friendly against United this summer. A proposal to play Monaco fizzled.