Weaver, who turns 27 on Sunday, yielded three hits and no walks while striking out five, throwing 77 pitches as the Angels clinched the season series against the Athletics in front of 14,554 at Oakland-Alameda County Coliseum.
"He's one of the better pitchers in the game," A's manager Bob Geren said, "and he was on tonight."
Weaver snapped a three-game losing spin with excellent snap on his breaking ball to go with a fastball that was alive and landing in the right places.
"I felt good," Weaver said. "I was working on my slider. It hadn't been as sharp as I want it the last couple times out. I was letting it go too early instead of getting out front.
"I wanted to go maybe another inning, but it was enough to take into the postseason having everything feel good."
Finishing 16-8 with a 3.75 ERA in 33 starts with career highs in innings (211) and strikeouts (174), the crossfiring right-hander is in line to work Game 2 of the American League Division Series against Boston at Angel Stadium.
Abreu will be batting second, behind Chone Figgins, and trying to jump-start an attack that has produced more runs than any offense in franchise history.
"That means a lot to me," Abreu said of his 30 steals alongside his 102 RBIs. "I was looking for that stolen base. I wanted to be in that club with Bobby Bonds [the only other Angels player with 30 steals and 100 RBIs in a season] and with Barry Bonds, too, doing it five seasons. Those two guys, everybody knows who they are. That's a special club."
His streak of 11 consecutive seasons with at least 20 steals is the longest in the Majors. He most recently reached 30 steals in 2006 when he divided time between the Phillies and Yankees.
Appearing in his 150th game on Thursday, Abreu reached yet another milestone, joining Willie Mays, Billy Williams, Pete Rose and Cal Ripken with at least 12 consecutive seasons with at least 150 games. Mays did it 13 times in a row.
"That's another special club," Abreu said, beaming.
Brian Fuentes nailed down his Major League-high 47th save by getting the final two outs after Kevin Jepsen had faltered in the ninth, yielding three singles while facing four men.
"I feel good, really good," Jepsen said. "I just have to get the right mentality back. That hasn't been me the last few times out."
Gio Gonzalez (6-7) struck out a career-high 10 for the A's, but the Angels managed to make hard contact.
Consecutive singles by Vladimir Guerrero, Kendry Morales and Mike Napoli produced two runs in the second.
After Napoli drove in Guerrero, Morales was credited with a steal of home, jumping over Kurt Suzuki's tag attempt, as the A's botched a rundown.
Rivera launched his career-best 25th home run in the fourth. Singles by Freddy Sandoval, Figgins and Torii Hunter produced another run in the fifth, with Hunter producing his 89th RBI.
Abreu scored his 96th run of the season after his steal on Gary Matthews Jr.'s pinch-hit single.
Rookie right-hander Sean O'Sullivan relieved Weaver and kept the A's in check with some excellent defense from Brandon Wood at shortstop and Sandoval at second base, and Darren Oliver worked a scoreless eighth. Run-scoring singles by Suzuki and Daric Barton in the ninth enabled the A's to avert a shutout.
The Angels are 10-7 against the A's, taking six of seven in Oakland, heading into the season's final two games.
Geren likes the chances of the division champs moving forward.
"I think they're always a strong contender, because they're so balanced," Geren said. "They can do everything. You run into tough pitching in the postseason, but they can manufacture runs; they go first-to-third better than anyone in the game, they steal bases. They have a nice formula."