D.C. United did not require an own goal to claim victory Saturday night. Left to its own devices, United persisted after a number of missed opportunities and defeated the New England Revolution, 1-0, on Luciano Acosta’s close-range volley in the 71st minute at RFK Stadium.

It was the first goal off a United player’s foot since July 19. The previous four tallies were on two headers and two own goals.

A banner in the supporters’ section read: “Own Goal We ♥ You”

MLS’s worst team through much of the summer, United (8-15-4) has parlayed several roster changes into a season-high three consecutive victories, all by shutouts, to keep alive its remote playoff chances.

“We still have a very big task ahead of us to get to where we want to be, but it certainly helps in every aspect around the club,” Coach Ben Olsen said. “New energy, we’ve added quality, and the players that have been here have all played up to their standard. That’s what has been missing over the course of the year.”

Olsen introduced another newcomer, Zoltan Stieber, to the announced crowd of 13,539 at RFK Stadium — and he was terrific. The Hungarian international logged 80 minutes on the left side, working well with Acosta and Russell Canouse and displaying a vision and prowess that bolstered the attack.

“We had some good combinations,” he said. “There was some good stuff there.”

Canouse, who, like Stieber, arrived from the German second division, put forth another strong performance in central midfield. Paul Arriola, a U.S. national team member who joined the club a few weeks ago, continued to mesh, and Acosta’s boundless energy kept United on its front foot much of the night.

The collective work probably is too late to squeak into the playoffs, but it has provided optimism heading into the 2018 campaign.

“A couple new faces, a couple of changes, have helped us a little bit,” Acosta said through an interpreter. “But more so than that, there is a confidence among us.”

United was in charge most of the first half but, per the usual, lacked finishing qualities, despite eight shots and six corner kicks.

Striker Patrick Mullins one-timed an eight-yarder well over the target after a promising build-up on the left side.

Revolution goalkeeper Cody Cropper did well to touch aside Mullins’s header and Stieber’s low bid but spilled a routine shot, which fell to Sean Franklin for a high miss.

United was under some stress in the second half and labored to regain its first-half rhythm.

Olsen’s first change, Lloyd Sam for Arriola, galvanized the attack. Three minutes after entering, Sam lifted the ball into the penalty area.

Kofi Opare won the header, directing a pass into the path of Acosta for a running left-footed volley inside the six-yard box for his team-high fifth goal of the season.

United hunted for another one, but Cropper bolted off his line on separate occasions to disrupt attempts by Stieber and Mullins in stride in the penalty area.

New England was busy in the attacking third but failed to seriously test goalkeeper Bill Hamid. Opare and Jalen Robinson (sixth career start) were solid in the heart of the back line.

The Revolution, playing without injured points leader Lee Nguyen, fell to 0-10-3 on the road and 8-12-5 overall, just one point ahead of surging United.

“Things are looking up,” Olsen said.

United notes: Steve Birnbaum and Patrick Nyarko (concussions), and Taylor Kemp and Bruno Miranda (hip injuries) were unavailable. … D.C. is off until Sept. 9 against visiting Orlando City.