Everidge hit a booming RBI double, Mark Ellis and Rajai Davis came up with infield singles, and a crucial error by shortstop Nick Green helped Oakland tie things up.
Two innings after that, the A's put together another two-out rally that thoroughly spoiled a special night for the Red Sox, who celebrated former slugger Jim Rice's recent induction to the Hall of Fame in a pregame ceremony to retire his No. 14.
Ellis doubled for his career-high-tying fourth hit, Davis broke the tie with another RBI single, and Adam Kennedy's career-high fifth hit helped Oakland to a stunning 9-8 victory in the second game of a four-game series at Fenway Park.
"That was a blast," said Everidge, who was called up from Triple-A Sacramento earlier in the day and arrived on a plane from Denver roughly 2 1/2 hours before the first pitch. "I've never had so much fun."
To say that Red Sox skipper Terry Francona wasn't of like mind is an understatement along the lines of saying Boston's bullpen is pretty good. Red Sox relievers hadn't allowed a run in 10 games since the All-Star break, and their 3.13 ERA for the season going into the game was the best in the Majors.
"We got to the ninth with 'Pap,' and a lot of things happened," Francona said.
What happened went down with A's manager Bob Geren bouncing from one television set to another in the visitors' clubhouse, from his office to the players' dressing area and back. He'd been kicked out of the game for arguing balls and strikes during Boston's five-run third inning against rookie right-hander Vin Mazzaro.
"I probably walked a couple of miles in here," Geren cracked.
Oakland's manager wasn't much for talking about what he did or said to get tossed, but he had plenty to say about his club's season-long habit of scoring late in games. It hasn't always translated to victories, but this victory was one of his favorites.
"It is," Geren said. "The odds of pulling that off are slim, and we did it. ... The one thing you learn is that you keep fighting until the end."
When Boston's bullpen takes over, the end is usually near and predictable. It brought a 24-inning scoreless streak into the game, but the streak ended when Ryan Sweeney's RBI single in the seventh cut the Red Sox's lead to 6-3.
Kennedy's RBI single in the eighth made it 6-4, but Mike Lowell's sacrifice fly off Brad Ziegler in the bottom of the frame gave Papelbon plenty of padding while working for his 26th save.
After a leadoff walk to Jack Cust, who took second base on defensive indifference, Papelbon retired Kurt Suzuki and Sweeney.
But Everidge jumped on the first pitch he saw and mashed it off the top of the Green Monster in left-center field to cut the lead to two runs; he scored when Green overthrew first base on a dribbler past the mound by Ellis; and after Ellis moved up to second on the error and stole third, Davis beat out a grounder into the hole between third and short for another infield single.
"The leadoff walk was what really set the tone for that inning," Papelbon said. "I had good stuff, and they were able to put together some at-bats. I felt like the only at-bat that I didn't really make a good pitch was to [Everidge].
"I have two outs there. I have to finish that game."
Instead, it was rookie righty Andrew Bailey who finished, picking up his 12th save despite allowing a run in the bottom of the 11th. Bailey wouldn't have been in the game were it not for another round of heroics from Davis, who drove in Ellis with a single to right, stole second and scored when Kennedy smoked a single to right of his own.
"He's been such a pleasant addition to our team," Geren said of Kennedy, who has three games with at least four hits since joining the A's on May 9 and is 22-for-47 (.468) over his past 11 games at Fenway. "It seems like you just keep thinking about how fortunate we are to have him."
Having Davis' speed available off the bench is a decent little luxury, too. He entered the game as a pinch-hitter in the eighth and went 2-for-3 to boost his batting average over the past 37 games to .319 (29-for-91).
Davis, though, was more stoked about the team's effort against the Boston bullpen than anything he did on his own.
"Hitting against the caliber of pitching is a challenge for us," he said. "To have success against that type of pitching should be a boost for everyone's confidence."