It was the lower third of the order that did the critical damage, as the offense dispatched Schilling before he could get an out in the decisive seventh.
Second baseman Maicer Izturis, 26, lifted his third homer of the season into the seats in right for the lead.
Catcher Jeff Mathis, 24, chased Schilling with a ringing double into the left-field corner, taking third on 26-year-old Reggie Willits' perfect bunt and scoring on Chone Figgins' sacrifice fly that rookie Brandon Moss juggled in left field, causing some confusion. The umpiring crew had it right, ruling that the runner can advance as soon as leather touches ball.
"I didn't know what happened until I got in the dugout," Mathis said. "I saw it hit his glove and took off."
When the Angels rallied in the fourth to draw even after Weaver yielded a two-run homer to Kevin Youkilis in the third, it was Casey Kotchman, 24, who rifled the two-run single past the feet of Schilling to get it done.
"I was trying to stay up the middle, not do too much, just make hard contact," said Kotchman, whose two-out single delivered the decisive run Sunday in Oakland. "They had the infield back, giving up a run, so I was hitting to the situation."
The upper classmen also delivered for the Angels, from the position players to the bullpen artists behind Weaver.
Figgins continued his torrid hitting with a single, triple and sacrifice fly. Orlando Cabrera singled and doubled. Vlad Guerrero's single followed by Gary Matthews' double set the table for Kotchman in the fourth.
Speier negotiated a scoreless seventh behind Weaver's six strong innings, moving to 1-2.
Scot Shields got into trouble in the eighth with a walk and single but escaped by striking out Mike Lowell and Coco Crisp around a flyout to left by Jason Varitek.
"The crowd got really loud after Shieldsy got that last strikeout," Kotchman said.
That left it to Rodriguez, and he was challenged on a rare error by Cabrera on Dustin Pedroia's one-out grounder.
After Youkilis flied out, K-Rod walked David Ortiz on a full count slider, leaving it all up to Moss -- in his Major League debut. The highly regarded young outfielder fell behind 0-2, looked at a ball in the dirt and another in his eyes, then went down swinging.
With Manny Ramirez's ejection after a fourth-inning strikeout leaving Moss in his spot, Mathis wasn't going to let Ortiz see anything in his lethal wheelhouse. The catcher made four trips to the mound during Big Papi's at-bat to keep the communication straight with K-Rod.
"Even though we were putting the tying run on base, we didn't want Ortiz beating us there," Mathis said, having called a 3-2 changeup that Big Papi let pass. New Englanders wish he'd taken a hack at it.
This was a much-anticipated return in Red Sox Nation for Schilling, who held the Angels scoreless across eight innings in April in the midst of Boston's three-game sweep. He experienced shoulder issues and shut it down after a loss to Atlanta on June 18.
The old warhorse came out throwing strikes, in his custom. This is a pitcher who will bury hitters if they go up taking a pitch or two, and the Angels came out swinging with feeling.
"He doesn't issue free passes," Kotchman said. "You have to be ready to hit."
It was an 0-1 pitch Kotchman slammed to center to tie the game, and Izturis was 1-1 in the count when he went deep. Mathis was 2-2 when he sent Schilling to the showers with his bullet into the left-field corner.
"It was a split," Mathis said. "I think he left it up. Any time you can square a ball up and get a hit off a guy like that, it's awesome."
Especially when it helps win a game and ends an 0-for-18 slide.
Coming off a pair of subpar efforts, Weaver was on top of his game, keeping hitters off balance with a changeup balancing his heater and breaking ball. His biggest outs of the night came in the fifth and sixth.
The Red Sox had two on with two out in the fifth when Ortiz went the other with a sharp grounder that Figgins deflected with a dive to his left. Cabrera reached the ball in a heartbeat and erased Big Papi by a half-step with a Gold Glove throw from the hole.
There is not a more accurate arm in baseball than Cabrera's, and he showed it yet again when it counted.
In the sixth, Weaver again was in trouble after a pair of one-out singles, but he reached back and struck out Varitek and Crisp, departing to a roar from the sellout throng.
The man calling those pitches was young Mathis, who continues to earn gold stars from teacher and manager Mike Scioscia with his pitch selection and what in prize fighting is known as ring generalship -- the ability to stay cool when the heat is on and stay out of trouble with the right decisions.
For Mathis and all the kids of Anaheim, it was a very good night in every respect.