Wei-Yin Chen (11-7) gave up one run, nine hits and a walk in six-plus innings for the Orioles, who moved 10 games over .500 (63-53) for the first time since June 24. Chen allowed at least one hit in each inning but was effective in minimizing the damage.
Baltimore is 7-3 against Boston this year, including 5-1 at Fenway Park. The Orioles have won the season series against the Red Sox only once since 1996, going 10-9 in 2004.
The trend seems to have reversed, and the Orioles can only hope it lasts.
"We've been playing really well against them all year," said Chris Davis, who had two hits and an RBI. "It was big for us to get the win and kind of set the tone for the series."
This isn't the same Boston club that lost in Baltimore on the final day of the season last year to fall out of the playoff picture.
This Red Sox team is 57-60, and Dustin Pedroia acknowledged after the game that there were a series of meetings in New York last month to discuss the team's decline under first-year manager Bobby Valentine.
"I know the coaches had a meeting, Bobby had a meeting, we all had a meeting," Pedroia said. "Basically when I spoke I said we all had to be better. That means the owners, Bobby, coaches, especially the players. I have had one problem with Bobby earlier in the year and I went into his office and talked to him like a man and he talked to me like a man. And we've been great. We've had a great relationship."
Pedroia said Valentine should keep his job.
"I don't think Bobby should be fired," he said. "Listen, we haven't played well and I am not going to blame anything on Bobby and I don't think anybody else is. It's on the players, man. Last year wasn't on (manager Terry Francona). I know he took it hard. We all did. It's on the players, man."
Beckett (5-10) surrendered six runs and six hits, including two home runs, in 5 1/3 innings.
"You have to keep the ball down," he said. "This isn't a real friendly ballpark (for pitchers)."
It's been a nightmare season for the right-hander, 1-6 in 12 starts since May 20. In his past two outings against Texas and Baltimore, Beckett has yielded a combined 14 runs and five homers in 10 1/3 innings.
Reynolds hit a solo shot off Beckett in the fifth and greeted Mark Melancon with a three-run drive in the sixth. After totaling 113 homers over the three previous seasons, Reynolds has only 11 this year. It was his first multihomer game since last Sept. 21, when he connected twice against Beckett.
Playing in his fifth major league game, Baltimore's Manny Machado was held hitless for the first time. But he made two fine plays at third base, where he has yet to make an error.
Boston stranded 12 and went 1 for 10 with runners in scoring position, a shortcoming fueled by cleanup hitter Adrian Gonzalez. He made the final out in the first, third and fifth innings, stranding a runner on second or third each time, and finished 0 for 4 with a walk.
Quintanilla hit Beckett's first pitch of the third inning over the right-field wall to put the Orioles up 1-0. He has four homers this season (including one with the Mets), after hitting only two in 227 games before this year.
Pedroia tripled with two outs in the fifth before Gonzalez grounded out. In the bottom half, Reynolds hit an opposite-field drive over the right-field wall to put Baltimore back on top.
Reynolds' homer, on Melancon's first pitch, capped a five-run sixth.
A moment of silence was observed before the game for former Boston star Johnny Pesky, who died Monday. ... The Orioles placed LHP Troy Patton (ankle) on the 15-day DL and recalled RHP Steve Johnson from Triple-A Norfolk. ... The Red Sox activated RHP Andrew Bailey (thumb) from the 60-day DL. He got the last out in the eighth. Boston traded C Kelly Shoppach to the Mets following a waiver claim. Ryan Lavarnway started behind the plate for Boston and went 1 for 4. ... Boston's Jacoby Ellsbury singled in the first inning to extend his hitting streak against Baltimore to 37 straight games, the longest by a Red Sox player against one team. ... Beckett has a strikeout in each of his 299 major league games, the second-longest streak to begin a career since 1900 behind Dwight Gooden (349). ... Rookie Miguel Gonzalez starts for the Orioles on Wednesday night against Boston's Aaron Cook, who makes his first career appearance at Camden Yards.