Schilling (2-1) went eight dominant innings, giving up four hits and a walk while striking out four.
Orlando Cabrera, with a double and single, and Howie Kendrick, with two singles and a walk, were the only Angels to reach base against Schilling, who allowed a runner to advance to scoring position only three times.
Hector Carrasco, replacing Kelvim Escobar (on the 15-day disabled list with shoulder irritation) in the rotation, struck out the first two hitters he faced before the Red Sox began working counts, draining his energy and testing his patience with long at-bats.
It started with a full-count walk to David Ortiz in the first inning after Carrasco felt he had the big man struck out with a fastball on the corner.
"It was right there," Carrasco said. "I had a hard time using my corners. I didn't get anything [from home-plate umpire Tim Timmons]. It's hard pitching in that weather, and when the umpire squeezes you ... it's not easy.
"My control felt good. I was throwing pitches right down the middle. When he started squeezing me, I got mad."
Carrasco made it through two innings unscathed despite three walks and a hit. But Boston got to him for two unearned runs in the third on an Eric Hinske triple, two walks and a two-base fielding error by a man generally considered the Angels' premier defender.
Carrasco thought he was out of the inning when Jason Varitek smacked a line drive in the direction of Matthews, who looked uncomfortable reading the ball before he got to it and had it bang off his glove hand, allowing two runs to score.
"It was knuckling a little bit and looked like it had some topspin going down," Matthews said. "It's a play I've made before. It's a tough play, and it came at a bad time. It kind of started the floodgates.
"It hit the heel of my hand. It didn't feel great. I would have felt better if it ended up in the pocket of my glove. It cost us a couple of runs."
Those were all the runs Schilling needed, but the Red Sox got him six more, four of them produced by Ortiz with a sixth-inning RBI single against Chris Bootcheck and a three-run homer in the eighth against Greg Jones. Ortiz has seven RBIs in the first two games of the series.
By the time his day had run its course after 3 1/3 innings, Carrasco -- who threw 44 pitches in the first two innings and 79 overall -- had yielded three runs (one earned) on two hits and a career-high six walks, with four strikeouts.
"Hector was trying to get into good zones early," manager Mike Scioscia said. "The ump had a tight zone ... and it's a fine line when you are behind in the count and you've got to keep trying to make pitches. It becomes a Catch-22. You're trying to make pitches in hitting counts, you have to be fine with it and you put a lot of pressure on yourself.
"Hector pitched his heart out, and we botched the ball in center. As much as they were getting guys on, we could have been tied through three innings."
Reviewing video, Carrasco was convinced that Schilling -- a man with 209 career wins -- was given strikes on virtually identical pitches that were called balls for him.
Schilling does own the neighborhood. He's 11-1 in his past 16 starts at Fenway Park, and his .765 winning percentage is the highest since 1957 among pitchers with at least 300 innings in the historic yard.
"Nothing I can do," Carrasco said, shrugging. "Nobody's perfect. It's over. Schilling threw a couple pitches, same pitches I threw, and I [didn't] get that call. It's OK. He pitched a good game."
Matthews, the Angels' leadoff catalyst, was as disappointed with his offense as with the glove that has already saved the pitching staff a number of runs in the young season.
"I felt pretty good off him," Matthews said of Schilling, after going hitless to shave his batting average to .227. "I got some pitches to hit. It really chaps you. It's frustrating when you don't do much with it."
The Angels' struggles run through the ranks. They've produced a total of 16 runs in the past seven games, and only four in the past three outings.
"Right now there are some adjustments guys are trying to make," Scioscia said. "We're in a little funk. We've had a tough time the last four or five games getting any kind of lead."
Since scoring the first run of the series against Tim Wakefield in the fourth inning of Friday night's game, the Angels have been blanked while giving up 18 runs.
That adds up to two bad days in Beantown, any way you calculate it.