D.C. United could ill afford to drop points at RFK Stadium on Sunday evening, not after losing two straight in dour fashion and not with a formidable two weeks of regular season and international soccer looming.

Three points required, three points achieved.

United answered Colorado’s spectacular equalizer early in the second half with a vigorous demonstration in notching a 4-2 victory over the Rapids before 12,814, including mayoral candidate Muriel Bowser.

Luis Silva scored twice, Chris Rolfe and Fabian Espindola added one apiece and Taylor Kemp, in his second start of the season, offered two assists in place of the injured Chris Korb.

“Our response was fantastic,” Coach Ben Olsen said. “It was one of the better responses out of the team this year. We took it to another gear and basically took the game over. We played some really good stuff.”

The timing was ideal. United (12-7-4) had lost a pair of away matches for its first losing streak since March, and with CONCACAF Champions League group play starting Wednesday at home and MLS matches at contenders Kansas City and Los Angeles afterward, D.C. needed this one.

“Every game now is crucial for us, and coming off the last two results, it’s a good feeling,” midfielder Davy Arnaud said.

With Perry Kitchen returning from suspension and the attack compensating for Eddie Johnson’s ban, United set the terms right away.

In the 12th minute, D.C. went ahead on Silva’s first strike. Kemp initiated the sequence, stepping up to disrupt Colorado’s counter and taking possession. His confident through ball met Silva in stride entering the penalty area.

Silva’s sharp cutback sent Drew Moor twisting away and created the space to beat advancing goalkeeper Clint Irwin.

“We have a very unselfish team,” said Silva. “We see a player open and we try to play that ball. It showed today, starting with Taylor seeing me open.”

Kemp’s initiative and pass delighted Olsen, who had watched the former Maryland Terrapin struggle in his first start of the season two weeks ago in Houston.

“Tonight was a big step for him,” Olsen said.

To make matters worse for the Rapids, Moor remained down with a sprained right knee. He was taken off by stretcher and replaced by rookie midfielder Jared Watts.

Bill Hamid preserved the lead heading into intermission with a sensational save on Vicente Sanchez in the 45th minute.

Early in the second half, Deshorn Brown caused problems with a pair of threats before Dillon Serna scored the equalizer with a glorious strike from 30 yards.

On Hamid’s clearance, Watts won a header in his own end, powering the ball past United’s backline.

It took a big bounce into the path of the 20-year-old Serna, who waited for the ball to drop to knee level before unleashing a drive that roared over the leaping Hamid and dipped into the net.

Espindola tried to answer, chipping off the crossbar and getting ruled offside when he appeared onside for a breakaway.

The persistence paid off in the 67th minute.

With right back Chris Klute keeping him onside, Silva slipped into space in the box and beat Irwin by one-timing Sean Franklin’s entry pass from eight yards.

The clincher came 14 minutes later. Kemp beat two Rapids on the left wing and crossed to Rolfe for a sliding one-timer from 17 yards, a low effort with perfect placement to the right corner.

Espindola joined the fun in the 86th with his eighth goal, collecting David Estrada’s cross in the clear and ripping a 15-yarder past Irwin.

Brown scored on a short header in the first minute of stoppage time.

Soccer notes: With Bowser in attendance, fans raised a giant banner before kickoff — “Every Loyal Washingtonian Deserves a Home” — in an effort to encourage the approval of a new stadium at Buzzard Point.

Bowser watched in the director’s box with United managing partner Jason Levien. . . .

The Washington Spirit (10-9-5) finished fourth in the National Women’s Soccer League and will visit the first-place Seattle Reign (16-2-6) in a semifinal Sunday.