Price struck out 10 over six sparkling innings to get Boston started on its 12th shutout of the season, and the Red Sox beat the Baltimore Orioles 5-0 Saturday in the opener of a split doubleheader.

The Red Sox have won eight of their last nine games and 12 of 14 to improve their big league-best record to 83-35. The twinbill was caused by a rainout on July 25 — before the bad weather came that night, Boston led 5-0 in the second inning.

Jackie Bradley Jr. hit two solo homers and Eduardo Nunez contributed a two-run drive, but Price hardly needed all that support on a day in which he scattered five hits and didn’t issue a walk.

“He was outstanding,” Boston manager Alex Cora said. “He is in a good place right now, physically and mentally.”

Price (12-6) threw 94 pitches on a sweltering afternoon to win his sixth straight start against Baltimore. The lefty had at least one strikeout in every inning and did not allow a runner past second base.

“He understands how important he is for us,” Cora said. “With the tough conditions out there, for him to go six today that was great.”

After Price left, three relievers combined for three hitless innings. With a dozen shutouts, the Red Sox are tied with the Cubs, Indians and Pirates for the major league lead.

“A good win for us after a very long game last night,” Price said.

After the Red Sox won 19-12 on Friday night, both teams were quiet offensively until the Red Sox broke through with a flourish against rookie Jimmy Yacabonis (0-1) in the fifth inning.

Xander Bogaerts led off with a single and Nunez hit a 3-0 pitch inside the left-field foul pole. One out later, Bradley lined an opposite-field drive to right.

That was all the offense the Red Sox required with Price in peak form.

Bradley homered in the ninth, his first multihomer game of the season and third of his career.

Adam Jones had two hits for the Orioles, who are 2-12 against Boston. Baltimore (35-82) was officially eliminated from contention in the AL East on Friday night and on Saturday clinched a second straight losing season.

Recalled from Triple-A Norfolk as the 26th man for the doubleheader, Yacabonis gave up three runs over 4 2/3 innings to absorb his first major league loss.

“He’s a work in progress,” manager Buck Showalter said. “Like a lot of our young pitchers, he’s growing a little bit from the experience he’s getting.”

Yacabonis allowed only one hit until it all came apart in the fifth.

“Just a couple of pitches,” he lamented. “If I execute them a little bit better then I probably put a zero up that inning. At least I got it to the fifth. The first four were good.”

TRAINER’S ROOM

Red Sox: C Blake Swihart (hamstring strain) will begin his rehabilitative assignment on Sunday with Short-A Lowell, Cora said.

Orioles: OF Craig Gentry (ribs) went 1 for 5 with three strikeouts Friday night in a rehab assignment with Class A Frederick.

ON SALE

Chris Sale is expected to start Sunday after a two-week stint on the disabled list with shoulder inflammation. Cora said the ace could throw 100 pitches if he’s not too rusty.

UP NEXT

Red Sox: Hector Velazquez (7-0, 2.64 ERA) was picked to start the second game. Cora was hoping to get three or four innings from a right-hander, who usually pitches in relief.

Orioles: Rookie Jefry Ramirez (1-4, 5.66 ERA) makes his eighth career start in Game 2. His only big league win came against Boston.