Abreu homered in the bottom of the 10th inning Wednesday to give the Angels a 2-1 victory over the Kansas City Royals and their first three-game sweep since mid-June.
"It's not over for us," right fielder Torii Hunter said. "The fat lady, she hasn't sang yet."
Abreu sent a 1-1 pitch from Jesse Chavez (4-3) into the right-field seats with one out. The Angels rushed from the dugout to greet Abreu but stood back, giving him plenty of room to safely cross the plate.
Kendry Morales sustained a season-ending broken leg on May 29 while jumping on home plate during a raucous celebration of a walk-off grand slam.
"We have rules," Abreu said, referring to changes made after Morales' injury. "After I touched home plate, we celebrate. We still have our emotions."
The Angels have won five of six with Abreu leading off.
"Bobby really works the pitcher," Hunter said. "He gives you a chance to see what the pitcher is doing. He's hitting a lot better in the leadoff spot."
Brian Fuentes (4-1) pitched a perfect 10th to get the victory, the Angels' seventh walkoff win this season. It was their fifth sweep and first since June 11-13 against the Dodgers.
"We're definitely taking the field with more confidence," Angels manager Mike Scioscia said. "We're not playing perfect games, but we're keeping ourselves in it. Eventually the offense has to pick up."
Angels starter Jered Weaver struck out 11, giving him a major league-leading 182. He surpassed his career-high of 174 strikeouts last season.
"Weave's stuff wasn't as crisp as we've seen it, but it was his best job of pitching all season," Scioscia said. "His fastball command at times maybe wasn't as locked in. He changed speeds on his breaking ball and his changeup was tremendous."
Weaver made his longest outing of the season, giving up one run in eight innings.
"He's definitely been under the radar way too much this year," Kansas City starter Zack Greinke said. "He's in the top three or four pitchers in the American League and he's leading the league in strikeouts. He's just shutting down everyone. He dominated and he kept us off-balance the whole time."
Greinke also went eight innings and, just like Weaver, allowed one run and six hits. Greinke struck out six and walked one.
"Greinke was dealing," Abreu said. "He mixed up his pitches really well. He's not going to give you anything to hit, so you have to be aggressive with him."
The Royals went 2-7 on their West Coast trip, with seven games decided by two runs or less. They were outscored 34-17.
"Usually the team that pitches better wins," Royals center fielder Mitch Maier said. "We had plenty of opportunities with guys on base, but we didn't get big hits when we needed them, and that's the story of the series right there. Weaver's probably the most deceptive guy I've seen. He's tough to pick up and he mixes his stuff and throws all his pitches for strikes."
After his 11th strikeout to open the eighth, Weaver gave up consecutive singles to Maier and Billy Butler. Kila Ka'aihue popped out to second, then Weaver walked Wilson Betemit to load the bases. Weaver got out of it when Alex Gordon hit a dribbler down the first base line. Weaver grabbed the ball and tagged out Gordon.
It was Weaver's sixth career game with 10 or more strikeouts and fourth this season. His 121 pitches were a career high. ... Royals CF Gregor Blanco left Anaheim on Tuesday to be with his wife in Atlanta for the birth of their child. Four other Kansas City players have left the team at various times this season for their children's births. ... Royals 3B Josh Fields will begin an injury rehab assignment in the Arizona Rookie League. He's been on the DL all season after right hip surgery. ... Torii Hunter returned from his four-game suspension and started in right field for the Angels, saying, "I'm happy to get out of that correctional facility." CF Peter Bourjos got the day off and was replaced by Reggie Willits rather than move Hunter back to his old position in center. ... Angels pinch-hitter Howie Kendrick had his 12-game hitting streak end.