"When you come into this place you never know what's going to happen," he said. "I haven't had much success here. ... It was nice to mix in a win and get us back on track."
Weaver (16-3) yielded two runs and seven hits, struck out five and walked one. He was tagged for a season-worst nine runs in three innings during a 12-3 loss to the Rays last Friday.
Weaver was 1-3 with a 7.16 ERA in six career games at Fenway before Wednesday.
He got off to an unusual start when Dustin Pedroia reached after striking out on a passed ball with two down in the first. Weaver then fell while throwing a pitch to Adrian Gonzalez, who eventually struck out to end the inning.
"I slipped a little bit," the gangly 6-foot-7 Weaver said, smiling as he recalled the moment. "It's bound to happen with all the body limbs flying around."
Howie Kendrick hit a solo homer and Torii Hunter had a two-run single for the Angels, who have won the first two in a three-game set at Boston after getting swept in a four-game home series against Tampa Bay over the weekend.
Los Angeles slugger Albert Pujols left in the fourth inning with tightness in his right calf, and the team said he would have a precautionary MRI on Thursday.
Ryan Lavarnway and Mike Aviles had RBI doubles for Boston, which lost for the sixth time in eight games and fell to 6-14 in August.
Red Sox right-hander Clay Buchholz (11-4) matched his season high for runs allowed, giving up seven in 5 1/3 innings. The 12 hits allowed equaled a career worst, also done in a 4-1 loss at Baltimore on April 26, 2011.
"It's tough. Nobody comes here every day wanting to lose or thinking we're going to lose," Buchholz said. "It's just been happening that way. To have a team that everybody knows can be really, really good with the players that run out there every day, it makes it a little bit tougher knowing that also."
Los Angeles, which had lost 11 of its 14 previous games in Fenway before this week, goes for the sweep Thursday when C.J. Wilson faces Boston's Franklin Morales.
"C.J. wants to take the baton and pass it along," Angels manager Mike Scioscia said. "They know how important they are to us, and hopefully they want to keep it going."
Leading 4-2 in the sixth, Kendrick homered into the seats above the Green Monster. Maicer Izturis and Erick Aybar then singled, chasing Buchholz. Junichi Tazawa struck out his first batter before Mike Trout's single loaded the bases. Hunter followed with his two-run single, making it 7-2.
The Angels' bottom four hitters in the order went 10-for-16 with six runs scored.
"I didn't know we did all that," Kendrick said. "I think it's huge to have a different part of the lineup put up those kinds of numbers."
The Angels jumped in front 2-0 in the third. Chris Iannetta had an RBI single and the second run scored on Trout's double-play grounder.
Los Angeles made it 4-0 in the fourth when Mark Trumbo and Izturis each had an RBI single.
Consecutive RBI doubles by Lavarnway and Aviles cut Boston's deficit to 4-2 in the fourth.
Pujols pulled up running between second and third on Kendrys Morales' grounder to shortstop before gingerly going into the third-base bag. He then came home slowly on Trumbo's single, limping noticeably as he went to the dugout. He was replaced in the bottom of the inning.
Pujols went 2-for-2 and scored a run. ... Red Sox manager Bobby Valentine wouldn't say what his rotation was for this weekend's home series against Kansas City. There is speculation that Daisuke Matsuzaka could take Aaron Cook's turn in the rotation. Matsuzaka, on the 15-day DL with a strained neck muscle, was impressive in a rehab start for Triple-A Pawtucket on Tuesday, allowing one hit in seven shutout innings. "The reports were good," Valentine said. "Threw the ball good. Kept it down. Came out of it good — just a sore calf." ... The Angels placed OF Peter Bourjos on the 15-day DL with a sore right wrist and recalled RHP Garrett Richards from Triple-A Salt Lake. Scioscia said Richards, who went 3-2 with a 4.42 ERA in nine starts before being sent down on Aug. 2, will work out of the bullpen. "It's certainly a chance for him to fit more into a role, but we'll start with him in the middle and see where it goes from there," he said. "He still has that length (to start), but we'll see where it goes from there." ... Hall of Famer Carl Yastrzemski turned 73 on Wednesday. ... It was Buchholz's 100th career start.