BALTIMORE -- The Boston Red Sox moved another step closer to the American League East title on Thursday night.

Andrew Benintendi lined a tiebreaking single in the fifth, Hanley Ramirez added a solo homer, and David Price threw seven solid innings as the Boston Red Sox completed a four-game sweep of the Baltimore Orioles with a 5-3 victory.

The Red Sox (89-64) and Price (17-8) both have eight-game winning streaks. Boston improved its American League East lead over the idle Toronto Blue Jays to 5 1/2 games while slumping Baltimore (82-71) fell seven games back.

The Orioles now sit a half-game behind the Detroit Tigers (82-70) for the second AL wild-card spot.

Boston's magic number is five to clinch the division championship. The Red Sox play their final 23 games against AL East teams, and they already are 11-3 in that stretch, including winning the past eight.

"We focus on the task at hand," Boston manager John Farrell said. "The way we've responded, the way we've come back in some tight ballgames, the way we've won on the road, I think it says a tremendous amount by the guys in our uniform."

The Orioles lost their fourth straight and fell for the sixth time in eight games on an 11-game homestand.

Baltimore manager Buck Showalter wants his team to forget the four-game sweep and focus now on its final home series of the season, against the Arizona Diamondbacks, which starts Friday.

"When you are down, they are going to step on you, and when you're up, you are going to ride the flow as much as you can," Showalter said. "It's all about riding the good times and shortening up the bad times as much as you can, and we are going to try to shorten this one up starting tomorrow."

Benintendi's single in the fifth -- one day after his three-run homer broke open a 5-1 victory -- gave Boston the lead for good at 4-3. It came off Vance Worley (2-2), who was on in long relief because starter Chris Tillman gave up three runs and lasted only 1 2/3 innings.

The Orioles had just tied the game in the third on Trey Mancini's three-run homer. Mancini has homered twice in just seven major league at-bats since being called up earlier this week.

Ramirez homered off Donnie Hart to make it 5-3 in the top of the seventh. The Boston first baseman, who also had an RBI single in the first, likes how his team has come together at the right time.

"The good thing about this team is just everybody's together, and we've got everything," Ramirez said. "Young guys, veterans ... it's one team."

Price allowed three runs -- all on the Mancini homer -- and scattered six hits. He struck out five and walked just two. His last loss came on Aug. 7.

"I felt like I made pitches when I needed to, with the exception of the third inning," Price said. "That was a big win. We've played good baseball, and this is the time of the year when you want your team to get on a roll the way we have."

Koji Uehara took care of the eighth inning, and Craig Kimbrel earned his 29th save with a perfect ninth.

Boston took a 1-0 lead with a two-out rally in the first. Mookie Betts singled and moved to second when David Ortiz walked. Ramirez then drove in Betts with a single to center as the Red Sox forced Tillman to throw 35 pitches in the inning.

The Red Sox added two more runs in the second. Jackie Bradley Jr. led off with a triple and scored when Sandy Leon followed with a single.

Tillman later allowed a single and walk to load the bases before Ortiz walked for a 3-0 lead. That ended Tillman's night, although he escaped with a no-decision.

"I was just mechanically bad tonight," Tillman said. "The more I tried to make an adjustment, the worse it kind of got for me. I just couldn't hit on (a) consistent basis. I'd hit one and then miss three. It wasn't good."

NOTES: RHP Dylan Bundy will start the series finale against the Arizona Diamondbacks on Sunday, according to Orioles manager Buck Showalter. RHP Yovani Gallardo and LHP Wade Miley will start the first two games of the series. Miley will leave the team after Sunday to go on paternity leave and should rejoin during the subsequent road trip. ... The Orioles pushed back the start of RHP Kevin Gausman (intercostal issues) and hope he will be ready to go on Tuesday or Wednesday. ... Rookie LHP Jayson Aquino (viral infection) was not available for the Orioles for a second consecutive game. ... Boston manager John Farrell sat SS Xander Bogaerts to give him a break. ... Red Sox RHP Steven Wright (right shoulder strain) threw from 60 feet Thursday, and if all goes well, he will throw from 120 feet Friday and Saturday. If that goes well, a bullpen session Sunday morning comes next, moving him closer to returning.