Braden picked off Chone Figgins in the first inning, Suzuki threw out the Angels' career base stealer in the third and Cust cut down a runner going from first to third -- the Angels' specialty -- in a 2-1 victory against the AL West leaders on Monday night.
"Our defense got three extra outs, which was nice because it gave Dallas another inning," manager Bob Geren said after his team won its sixth consecutive series opener. "He got a whole inning's worth of outs on the bases. It was a heck of a job by him and the defense."
The Angels, 54-11 when they score first, sent four batters to the plate in the opening inning and three of them had hits -- but they still came up empty.
Figgins led off with a single, but Braden recorded his fourth pickoff before throwing his next pitch.
"It was just a good move," Figgins said. "I didn't know he had it. It surprised me."
It was the 26th pickoff by the Oakland staff, which leads the majors. Rookie Greg Smith, scheduled to start Tuesday night, has 14 of them.
"As a staff, we really try to stress that and give us every opportunity to get outs any way we can," Braden said. "As a guy who's not going to light up the radar gun, you look for outs in other ways when you're struggling or even when you're going good. One of the facets of my game I like to practice is controlling the running game and giving Zuke a chance to throw a guy out when he does decide to take off."
Erick Aybar singled after the pickoff, then tried to advance to third on Torii Hunter's two-out single to left and Cust gunned him down.
Angels base runners have gone from first to third on a single 90 times, a major league high.
"It was awesome," Braden said. "I mean, nobody wants to be in a hole right out of the gate, especially against these guys. What are they, 148-2, something like that? It's ridiculous. You know that when they get guys on, they're going to get them over and get them in. So you try to minimize that. It was real good getting out of that without a blemish."
Angels manager Mike Scioscia said Aybar's hesitation rounding second base is what ultimately cost him.
"It's really base running 101," Scioscia said. "If he runs through second with aggressiveness, he's going to make it to third. He was reading the play. It took a perfect throw, but still, Erick has to run hard to have a chance. When he got around the bag he turned it on, but obviously it was a step too late."
The Angels ran themselves into another out in the third, when Figgins attempted to steal second and was thrown out for the 10th time in 35 attempts this season.
"Everybody in the world knows he's going to run, and he's usually successful," Suzuki said. "So doing a good job of holding that guy on, controlling him on the bases and not letting him wreak havoc on the infield is real important."
Braden (4-3) allowed a run and seven hits over seven innings without recording a strikeout or walk.
"I was happy about the way I was attacking the strike zone and pitching to contact," he said. "Before I was a guy who wanted to light up the Ks. But now I'm a guy who really just tries to let the defense do their job."
The 25-year-old left-hander, who made his first nine appearances this season in relief before going to Triple-A Sacramento, is 3-3 in seven outings since being inserted back into the rotation on July 22. Last year, he was 0-8 with a 7.91 ERA over his final 13 starts after beating Baltimore in his big league debut.
"The difference is just his strike-zone command," Geren said. "I think his confidence is going up each time he goes out there. His velocity might be up just a tick from last year, and he's got a better feel for his changeup."
Brad Ziegler followed Joey Devine out of the bullpen and pitched a hitless ninth for his fifth save in five chances. The rookie right-hander has allowed only two runs in 45 innings.
Jered Weaver (10-10) allowed two runs and three hits in seven innings and struck out eight.
Daric Barton hit a home run in the third, which gave the A's a 1-0 lead. Frank Thomas scored Oakland's second run on a wild pitch in the fourth after drawing his second walk and advancing on Jack Hannahan's double.
Mike Napoli hit his 14th home run on Braden's first pitch of the sixth. Napoli is 9-for-41 against Oakland pitching since the start of last season, and six of his hits have been home runs.
Angels switch-hitter Gary Matthews Jr. was in the starting lineup for only the third time in 13 games, which could help explain why he came to the plate his first time up with a helmet that had the ear flap on the wrong side. ... Angels RHP Francisco Rodriguez was named AL player of the week for the first time in his seven-year career after notching his major league-leading 50th save.