Jake PeavyBOSTON — The Red Sox returned home Monday following a 4-6 road trip with reason to be optimistic.

The Red Sox ended their trip with back-to-back victories over the New York Yankees at Yankee Stadium, and Boston’s offense showed life in Sunday’s series finale with an eight-run, 12-hit output.

Jake Arrieta stopped the Sox dead in their tracks.

Arrieta nearly tossed a no-hitter as the Red Sox suffered a 2-0 loss to the Chicago Cubs to begin their 10-game homestand.

Let’s go over how everything unfolded.

— Arrieta was sensational, dominating from the second he took the mound.

Arrieta made a bid to become the first pitcher since Jim Bunning in 1958 to no-hit the Red Sox at Fenway Park. Stephen Drew broke up the no-no with a single into right field with two outs in the eighth inning.

Arrieta threw a career-high 120 pitches and struck out 10 in his 7 2/3 hitless innings. He received a standing ovation from the Fenway crowd upon exiting the game — something Arrieta said gave him goosebumps.

Monday’s performance marked the second straight start in which Arrieta produced a no-hitter through at least six innings. He owns a 0.92 ERA (four runs in 39 1/3 innings) over his last six starts.

— Every time it looks like the Red Sox’s offense is turning a corner, the unit lays an egg.

The Sox only mustered two hits Monday, as A.J. Pierzynski followed Drew’s eighth-inning single with a pinch-hit single in the ninth inning. Mike Napoli, who walked in the fifth inning, was Boston’s only other baserunner.

“Every time we seemingly put together a couple of quality performances back-to-back, it’s been difficult to extend,” Red Sox manager John Farrell said. “You can’t pinpoint any one reason, but still, it is a little frustrating, particularly where we are with our record and our status or place in the division — trying to get some momentum going. But you credit a solid performance (Monday night).”

— Jake Peavy, who had an awful June, ended the month with a quality performance.

One mistake was enough, though, as Nate Schierholtz’s two-run homer — preceded by a two-out walk to Welington Castillo that featured a borderline 3-2 pitch — represented the game’s only offense.

Peavy allowed two earned runs on five hits over six innings. He struck out seven, walked two and threw 109 pitches (73 strikes).

— Peavy has had a rollercoaster season, but for the most part, he has received very little help from the offense.

Peavy received no runs of support for the third time this season Monday. He has had two runs of support or less 13 times in 17 starts, resulting in a 1-7 record to go with his 4.82 ERA.

“Quality starts most of the time around here you’ll take it and it’s plenty good enough to win for years now in this uniform,” Peavy said. “It’s just one of those years where those quality starts have been matching up on days we haven’t scored a whole lot and your record doesn’t look so hot. None of that matters to me. I’m going to turn the page and be ready for Baltimore on Sunday and try to be as good as I can be to give us a chance to beat them.”

— Mookie Betts played center field and went 0-for-3 in his Fenway Park debut. He also misplayed a ball in the second inning, allowing it to drop near the base of the center field wall even though it looked catchable.

— Mike Carp played in his third rehab game with Triple-A Pawtucket. He played the first five innings at first base and went 0-for-3 with a strikeout.

Andres Torres and Alex Hassan each drove in four runs for the PawSox. Anthony Ranaudo threw seven shutout innings, and he now is 4-0 with a 0.85 ERA in five starts since June 6.