Weaver won his fifth consecutive decision on Sunday versus Tampa Bay, as he held the Rays to a pair of runs and six hits in six innings. He also walked four batters, but improved to 12-6 nonetheless, while lowering his ERA to 3.59.
The right-hander has pitched to a 3.46 ERA in his last nine outings.
"You can't complain too much when [the bats] put five runs on the board there in the first," said Weaver. "It makes the starting pitcher's job a little bit easier."
Weaver has also been pretty solid in L.A. of late, going 2-0 with a 1.74 ERA in his last five starts at home. He is 3-3 with a 1.99 ERA in nine career home starts versus the Red Sox.
Los Angeles enters this series on a bit of a sour note after dropping the final three games of the Freeway Series to the Dodgers, including Thursday's 7-0 setback.
C.J. Wilson (8-8) was charged with six hits and four runs across 5 2/3 innings. He's winless in his last five appearances.
"C.J. had a tough time with his command early," Angels manager Mike Scioscia said. "He made some adjustments, but used a lot of pitches and had deep counts. They (Dodgers) did a good job on the mound the whole series against us. We didn't swing the bats well the last couple of games."
The Angels lost their third in a row for first time since a season-high four- game skid May 30 - June 3. The Angels are now three games behind Oakland for first place in the AL West.
Boston, meanwhile, has lost four of five after a series loss in St. Louis that culminated with a 5-2 setback on Thursday. Brandon Workman (1-5) surrendered four runs on six hits and two walks over 5 1/3 frames for Boston, which has dropped seven of its last nine contests.
"That got me today, I put up a three-spot in the first," Workman said. "I threw well after the first."
Hoping for a better effort tonight, the Red Sox will turn to right-hander Allen Webster, who is 1-1 in two starts with a 6.75 ERA. Webster continued to struggle with his command in a loss to New York on Saturday, as he allowed four runs and two hits and walked six batters in just 2 2/3 innings.
He has walked 11 batters in two starts since taking Jake Peavy's spot in the rotation.
"It was just my fastball," Webster said after the loss to the Yankees. "If I could have found my release point on my fastball, I could've gotten my other pitches to work behind it."
Boston split six meetings with the Angels last season.