Both are headed to next week's All-Star Game along with teammates Jonathan Papelbon, who struck out the side in the ninth to earn his 21st save in 23 opportunities, and Tim Wakefield, who pitches the series finale on Wednesday night.
"Obviously I blew it in April," said Beckett (10-3), "but I feel like I've had a good couple of months, really getting back on track."
His ERA was 7.22 at the end of April but 3.62 now. On Tuesday, he gave up two runs, six hits and a walk with four strikeouts in 6 2/3 innings.
"He's one of the best," Boston manager Terry Francona said. "He's fearless. Our guys look up to him. I think he enjoys that responsibility."
Beckett improved to 5-0 in his eight Fenway Park starts this year.
"I love pitching here," he said. "It's awesome to pitch in front of a full house every night."
With Wakefield also at 10-3, the Red Sox are the only team with two 10-game winners.
Bay, the top vote-getter among AL outfielders for next Tuesday's All-Star Game, had a much better start than Beckett with a .324 batting average through May 10. That fell to .259 by last Saturday, but Bay is 4-for-8 since then and hit his 20th homer to tie the game 1-1 in the second inning Tuesday.
"When guys are locked in," he said, "the ball looks like a beach ball and stuff. And then there's the exact opposite of that where it looks like an aspirin coming out of a shotgun and you're really battling up there.
"You know it's not going to last forever."
The Red Sox got nine hits off Dana Eveland (1-3) and four relievers one night after managing just two hits off rookie Brett Anderson in his 6-0 complete-game victory. That was the third loss in four games for the team with the AL's best record (50-33).
Eveland, recalled from Triple-A Sacramento when Dallas Braden went on the bereavement list Monday, was designated for assignment after the game. He allowed four runs and six hits in 2 2/3 innings.
"It wasn't that he had no command," Oakland manager Bob Geren said. "It was that when he got ahead [in the count] he didn't keep it."
Scott Hairston broke Beckett's streak of 23 innings at Fenway without an earned run with a solo homer in the first, two days after being traded from San Diego, where he hit 10 homers.
"We put some good swings on him, but obviously when he's on he's on," said Hairston who made his first visit to Fenway since 1984 when he was 4 years old and his father, Jerry, played there for the Chicago White Sox.
Beckett left in the seventh after Kurt Suzuki reached on third baseman Kevin Youkilis' error and took second on an infield single by Ellis. Hideki Okajima ended the threat by retiring Kennedy on a groundout.
The Red Sox took a 2-1 lead in the second on Bay's homer and a double-play grounder by Nick Green that scored David Ortiz, who had doubled and moved to third on the first of Jason Varitek's two singles.
"I threw a fastball right down the middle when I was trying to go in on Bay," Eveland said. "I just really missed some spots."
Varitek's second hit drove in two runs in the third. J.D. Drew led off with a double and took third when Bay reached on a forceout at second. Bay stole second, Ortiz walked and Varitek singled.
Boston scored the final run on an RBI single in the sixth by Dustin Pedroia, who returned to the lineup after missing Monday's game to be with his pregnant wife, who was hospitalized after going into labor. Pedroia said Tuesday she was OK.
Oakland 1B Jason Giambi went 0-for-4 with three strikeouts and is 5-for-44 in his last 13 games. ... Boston 1B Aaron Bates, who made his major league debut Monday night, went 0-for-3 with two strikeouts and is 0-for-6 with four strikeouts in his two games.