Branko Boskovic (8) of D.C. United celebrates his first goal in 39 appearances. The goal gave United a 1-0 victory over Chivas USA. (Ned Dishman/GETTY IMAGES)

Everything broke D.C. United’s way over the weekend.

The other playoff contenders dropped crucial late-season points. Coach Ben Olsen continued to work his substitution magic. Branko Boskovic scored his first MLS regular season goal since arriving more than two years ago.

And most importantly, United won its third match in eight days, a 1-0 victory over Chivas USA in front of 11,770 spectators at RFK Stadium on Sunday evening.

The result extended United’s unbeaten streak at home to 15 and forged a third-place tie with the New York Red Bulls in MLS’s Eastern Conference, just five points behind front-running Sporting Kansas City.

“We talked about nine points in three games as a goal,” Olsen said. “You go about working toward it and then when you get it, it feels good. We’ve put ourselves in a pretty good position.”

After slipping to sixth place, one spot out of the playoffs, United (15-10-5) has put itself four points clear of the Houston Dynamo and five of the Columbus Crew with four matches left.

The victories came against weak opponents — New England, Philadelphia and Chivas are among MLS’s worst — but to its credit, United put in determined performances and showed it could win without Dwayne De Rosario (season-ending knee injury).

United’s favorable schedule will continue the next two weekends with away matches against Portland (7-15-8) and Toronto (5-18-7). Piling up points would bring additional comfort heading into the season finales against playoff contenders Columbus and Chicago in late October.

“We want to create some separation and see how far we can get up in the standings,” defender Chris Korb said.

United labored to break down Chivas (7-15-7), which is winless in nine straight and has scored just 21 goals. But early in the second half, Olsen made a substitution that, for the third consecutive match, parlayed into a go-ahead goal.

Boskovic, who earlier in the week grumbled about playing time, had started the past two games but was in reserve Sunday. Seven minutes after arriving, he scored for the first time in 39 appearances.

Last weekend against New England, Lewis Neal broke a 1-1 tie seven minutes after replacing Boskovic. On Thursday at Philadelphia, Maicon Santos entered for Boskovic and, 10 minutes later, helped set up Lionard Pajoy’s winning goal.

On this night, Boskovic “did well calming us down and giving us good balls from side to side,” midfielder Chris Pontius said. “It eventually opened the game up.”

From the right side of the penalty area, Lionard Pajoy crossed toward the six-yard box. In a brave and dangerous act, Boskovic dived in front of center back Danny Califf and directed a header to the far corner.

Teammates pounced on him as if he were a teenager scoring in his pro debut, not a 32-year-old veteran with a European portfolio and national team experience with Yugoslavia and later Montenegro.

Boskovic missed most of the 2011 season with a major knee injury and had received inconsistent playing time this year. On Tuesday, he vented his frustration about Olsen’s decisions to remove him from matches early.

“I put this behind me,” he said Sunday. “I speak with Ben. I respect him. This is normal in a career. Everyone has moments like this.”

Said Olsen: “To me, it’s just a guy who wants to be on the field and wants to win. His attitude all week has been good. He is committed, even though I am sure he disagrees with me at times. . . . I’m glad he was the hero.”

Like the previous two victories, United had to withstand late pressure before recording consecutive shutouts for the first time this season. “Let’s not go crazy here. We could have had ties or losses in all three of these games,” Olsen said.