Matt Shoemaker, Chris IannettaBOSTON — The Red Sox’s offense has become a dating app. There’s a lot of flirting going on, even if no one’s getting any action at the end of the day.

Matt Shoemaker on Thursday became the latest pitcher to flirt with a no-hitter on the Red Sox’s watch. The right-hander carried a no-no into the seventh inning as the Los Angeles Angels put the finishing touches on a four-game sweep with a 2-0 win at Fenway Park.

“I don’t know the numbers. We’ve been in the sixth or seventh inning a few times this year with no-nos, so that’s never a good thing,”  third baseman Will Middlebrooks said after producing Boston’s lone hit. “But we always find a way to grind out a few hits here and there — tonight wasn’t that many. But we’ll be back at it tomorrow.”

Middlebrooks’ double with two outs in the seventh spoiled Shoemaker’s no-hit bid, but the 27-year-old rookie still was sensational. Shoemaker exited after 7 2/3 shutout frames in which he struck out nine and walked one. Red Sox starter Rubby De La Rosa countered with a pretty good effort, allowing just two runs over 6 2/3 innings, but Boston never stood a chance against Shoemaker’s crafty mound work.

“He was obviously making good pitches with all three pitches,” Middlebrooks said. “He had a good split, his slider was working, he was mixing a curveball in, too. Everything was just black away, black in, at the knees or below. He did a good job.”

Shoemaker plunked Brock Holt to begin his outing. He then retired 20 in a row before Middlebrooks — a .193 hitter battling hamstring tightness — ripped a 2-2 pitch into the left field corner. Shoemaker rebounded to retire Allen Craig, ending any potential threat and preserving the Angels’ two-run lead.

Shoemaker came back out to begin the eighth inning. He struck out Kelly Johnson and Xander Bogaerts before issuing a nine-pitch walk to Mookie Betts that ended the pitcher’s night at 116 pitches. It was another superb outing for Shoemaker, who is 5-1 with a 1.57 ERA over his last six appearances. It also was another victory for Shoemaker against the Red Sox, as he tossed three perfect relief innings while earning a win in the Angels’ 19-inning win over the Sox on Aug. 9 in Anaheim.

“A lot of strikes, very good split and was able to mix in a breaking ball — either early in the count or when he did fall behind — to slow us down,” Red Sox manager John Farrell said. “We couldn’t get anything going against him. He’s been very consistent for them. In addition to the extra-inning game out in Anaheim, he’s pitched very well against us.”

Shoemaker became the 11th starter this season to limit the Red Sox to three hits or fewer while tossing at least seven innings. He joined Chris Sale, Marcus Stroman and Jake Arrieta in surrendering only one hit in a start of at least seven innings against Boston. Arrieta lost a no-hitter in the eighth inning June 30 at Fenway Park, and Stroman lost a no-no in the seventh inning July 26 at Rogers Centre in Toronto.

Thursday marked the first time the Red Sox were one-hit at Fenway in a regulation game since April 11, 2007, when Felix Hernandez tossed a complete-game, one-hit shutout.

Guess who’s scheduled to oppose the Red Sox for the Seattle Mariners on Friday. Yup. King Felix.

Let the flirting continue.