After drawing even with a three-run seventh, the A's turned two walks, Scott Hairston's single and Daric Barton's run-scoring infield out into the decisive run in the eighth, pinning the loss on Rafael Rodriguez (0-1), while Brad Ziegler (1-4) claimed the win.
It ended with an Oakland double play. A strong throw from left fielder Hairston nailed Chone Figgins as the leadoff catalyst tried to advance on Bobby Abreu's fly ball toward the foul line.
Figgins, the American League leader in runs scored with 98, led off the ninth against A's closer Andrew Bailey and reached base on shortstop Cliff Pennington's error.
"I'm fine with that," Scioscia said of Figgins' aggressive play. "Figgy's going to steal 20 runs before he gets thrown out. They made the play. Give Hairston credit for putting the throw where it needed to be."
After a gritty performance by Weaver, the Athletics rallied against the Angels' bullpen. Two singles and a walk were yielded without an out by Jose Arredondo, who wild pitched one run home before Rajai Davis' two-run single against Rodriguez tied it at 3.
"Our options were out there," Scioscia said, meaning Arredondo and Rodriguez were all he had available besides closer Brian Fuentes, who waited in vain for a ninth inning to close.
Rodriguez was returned to Triple-A Salt Lake after the game to make room for new starter Scott Kazmir, who is scheduled to make his Angels debut on Wednesday in Seattle. Right-hander Trevor Bell remained with the big club and will join the middle relief corps after making four starts.
Weaver, bidding for his 14th win, kept the A's off balance and off the scoreboard for six innings, yielding four hits and two walks while striking out three.
"It was a battle all the way," said Weaver, the staff leader with 173 1/3 innings. "They hit a lot of foul balls and laid off some good pitches, and that got my pitch count up.
"I felt good, but it got away from us at the end. Our bullpen's been used a lot lately. That's baseball. We've just got to go out tomorrow and get it done."
Getting a rare start at shortstop with Erick Aybar taking a day off, Izturis doubled in his first at-bat before unloading his eighth homer of the season into the right-field corner in the fourth following a single by sizzling Kendry Morales.
The Angels had taken the lead in the third against Vin Mazzaro on singles by Howard Kendrick and Figgins and a sacrifice fly by Bobby Abreu.
Weaver was running up his pitch count on a sweltering night as he worked out of early trouble, getting big outs -- and strikeouts -- with his changeup.
He made the fourth his first 1-2-3 inning and followed it with a perfect fifth before Davis led off the sixth with a double. Davis reached third, but Weaver left him there, turning it over to the bullpen after making 119 pitches.
Davis made his presence felt in the seventh, when he slapped a single through the middle to cash in a pair of runs that tied the game.
Davis surfaced again in the ninth with his third hit in four innings, but he was stranded at second.
Shut down by iron man Michael Wuertz, who was making his 61st appearance, in the eighth after Ziegler had rolled through a perfect seventh, the Angels expired on Hairston's throw. Bailey's save was his 20th of the season.
Torii Hunter's 14-game hitting streak was snapped, and the Angels -- the Majors' best hitting club with runners in scoring position -- went 0-for-6 in those game-turning situations.
All the relief on a hot Saturday night was in the other dugout.