Hunter delivered three hits and a walk in a 7-2 victory while Hideki Matsui produced the knockout blow, a three-run homer off Josh Beckett.
"[I told them to] go out and play like it's your last [game]," Hunter said, offering a capsule summary of the session. "Give it your all. That's what we plan on doing the next 40-odd games."
Salvaging a happy ending to a dismal season series, the Angels released a Boston stranglehold spanning nine games, including six in a row at Fenway.
Swinging with feeling in the sixth inning after being shut down through five by Beckett, the Angels produced four consecutive hits, culminating in Matsui's bomb to right-center.
Improving to 13-8, Ervin Santana was the beneficiary, keeping his team in the game and then watching all of the runs arrive in the sixth and seventh innings.
"It's always nice when we score a lot of runs," Santana said, having turned things over to Kevin Jepsen after encountering problems in the eighth.
Jepsen dispatched Boston's 4-5-6 hitters, putting his premium fastball and offspeed stuff in the right locations after letting them wander in Wednesday night's distressing loss.
"It's always nice to come back the next day, get back on the horse, and go out and pitch well," Jepsen said. "I'd like to have saved all of Ervin's runs, but it felt good to get those outs."
After Beckett had held the Angels to two singles through five innings, Maicer Izturis started the uprising with one out in the sixth when he doubled past first base on a full-count fastball.
Alberto Callaspo banged another Beckett fastball on a 3-1 count off the Green Monster, scoring Izturis with the tying run. Hunter picked up an infield hit on a first-pitch fastball and Matsui followed suit, driving a 94-mph first-pitch heater into the Boston bullpen.
"Beckett had good stuff early on," manager Mike Scioscia said. "It took us a while to bunch some hits. Obviously, Hideki's hit was big."
Matsui's 16th home run was the exclamation point.
"Yeah, you don't make pitches, you don't get outs," Beckett said. "I made a bad pitch to Matsui. I was trying to go down and away, and it ends up [in the] middle of the plate, and he does what big leaguers do."
Matsui added an RBI an inning later, matching his season high with four, when the Angels scored three times on four walks and infield hits by Peter Bourjos and Howard Kendrick.
Ending an 0-for-16 drought, Bourjos hit a bunt single to get the rally started against Beckett, who gave way to Manny Delcarmen after walking Bobby Abreu.
Delcarmen yielded three walks and a run-scoring infield out by Callaspo before Scott Atchison came on and served a run-scoring hit to Kendrick.
Santana had kept the Red Sox out of scoring position before David Ortiz found a 2-1 changeup to his liking and sent it rocketing out of the park to right field. It was his 27th homer of the season.
Santana didn't allow another hit until Marco Scutaro's leadoff single in the eighth. Jed Lowrie, replacing Dustin Pedroia (sore foot) at second base, doubled to right, and Ortiz was hit on the foot with an 0-2 fastball.
Jepsen, focusing on keeping the ball down, retired Victor Martinez on a shallow fly ball. Adrian Beltre's sacrifice fly scored Scutaro, then J.D. Drew struck out to end the inning.
"Jep faced some good hitters there to minimize the damage," Scioscia said. "That was impressive."
Beckett was aided by superb defensive plays by Mike Lowell at first and Drew in right in the third, plays that deprived Abreu and Izturis of hits.
Beckett, who missed 56 games from May 19 through July 22 with a lower back strain, yielded six earned runs in 6 1/3 innings. He departed with a 6.67 ERA in 14 appearances, only five classified as quality starts. He is now 3-3.
Scioscia and the coaching staff had vacated the clubhouse before the game, and a number of voices were heard during the players' animated dialogue.
"Certainly, a meeting like that can raise a sense of urgency," Scioscia said. "It can be a negative or a positive. Some guys might try too hard, or a meeting might bring them to where they need to be.
"It's good when players get together. I think they took the field with a real sense of purpose. What it is, really, is making the field yours, which was what I think we did."
Hunter, Abreu and Matsui, the elders of the outfit, apparently took charge of the session, according to Santana.
"Mainly, it was the guys with [service] time doing the talking," Santana said. "It was a good meeting."
With the team heading to Minnesota, where he launched his career, to face the sizzling Twins, Hunter could look forward to some much-needed sleep.
"Those guys had our number this year," Hunter said, referring to the Red Sox. "We weren't ourselves. We'd be good a couple weeks, the Angels, then become the Bad News Bears. We have to stay consistent."