Kendall doubled with one out in the top of the 11th off Boston righty Julian Tavarez, scored easily on Kielty's single off the Green Monster, and after Kielty took advantage of a rare green light from the bench and stole second, Thomas added what turned out to be the difference maker with an RBI single to left.
Saarloos, a member of the starting rotation who was called into emergency duty as the eighth A's pitcher of the night, survived a rocky bottom of the frame to pick up his second save of the season as Oakland snapped a three-game losing streak and remained tied with the Rangers atop the American League West standings.
"We didn't end the first half the way we wanted to, and we knew this was going to be a tough series," Kielty said. "So to start the second half with a win like this is pretty sweet. Especially when so many guys came up big."
A's starter Esteban Loaiza matched a career high by walking six in addition to giving up six hits, but he managed to limit the damage before leaving with a pitch count of 109 after the fifth inning. Along the way, Loaiza established a pattern of stranding at least one runner in every inning that continued until closer Huston Street worked a perfect 10th.
"These guys are tough [outs]," A's manager Ken Macha said of the Sox, who drew 11 walks but left 15 men on base. "They work you hard."
Boston's Mike Lowell got the scoring started with a solo homer in the second, and Nick Swisher answered with a solo shot of his own in the top of the third, giving him 21 homers on the year and matching his rookie total of a year ago.
The Sox quickly reclaimed the lead in the bottom of the frame, getting a leadoff double from David Ortiz, an RBI single from Trot Nixon and an RBI groundout from Lowell, but an error by a sure-handed All-Star helped the A's knot things back up in the seventh.
Singles by Antonio Perez and Kendall opened the game-tying sequence. Both runners advanced on a groundout by Swisher before Boston second baseman Mark Loretta whiffed on a grounder by Kielty, allowing both runs to score.
"He just didn't look it into his glove," said Red Sox manager Terry Francona. "Probably happens one out of every thousand. ... That's part of the game."
A huge part of this game was A's relievers Chad Gaudin, Brad Halsey, Justin Duchscherer, Kiko Calero and Street holding the Red Sox scoreless for five innings after Loaiza's departure.
Street, who came on with two on and one out in the ninth, was perfect in the 10th, and lefty Scott Sauerbeck took over to start the bottom of the 11th and retired Ortiz on a foul pop.
Saarloos, who used to close on Fridays and start on Sundays while playing for Cal-State Fullerton, came on to get Manny Ramirez on a grounder to Perez at third, but Gabe Kapler followed with a tremendous at-bat, fouling off several full-count pitches before working a walk.
After taking second base on defensive indifference, Kapler scored on a single by Jason Varitek, but the suspense finally ended on a comebacker by Lowell, four hours and 23 minutes after the game's first pitch.
Earlier this year, Saarloos recorded a win and a save in the same week. He remains on track to start against the Orioles on Monday, so there's a chance he can match the feat in a five-day span.
"Let's do it again," he said. "Sounds good to me."