"He's a game-changer," Jackson said. "I've seen him make a play similar to that in Triple-A when I was in Nashville. I knew he had it in him but man, plays like that, if those don't get you fired up then I don't know what does.
"First of all, to make the catch. And after that the throw. That's what he's capable of doing. He's a playmaker for sure. I'm sure you'll see much more of it."
Marcus Semien homered twice and Khris Davis also connected as Oakland won for the eighth time in 10 games. The A's also stayed 1 1/2 games ahead of Seattle for the second AL wild card.
Jackson (4-2) allowed three hits and walked three in 7 1/3 innings. Ryan Buchter got two outs and Emilio Pagan finished the five-hitter.
But it was Laureano's play that caught everyone's attention.
"That's probably one of the more impressive things I've seen in baseball," Oakland left fielder Chad Pinder said.
"He knew exactly what he was doing. He put it right on the money."
Semien had three hits, scored three times and drove in four runs. He hit a three-run shot in the second and a solo drive in the fourth.
Davis hit his 34th homer in the third, a solo drive to right that made it 5-0. Davis has 13 homers in his 20 games since the All-Star break.
Los Angeles had won four in a row. Tyler Skaggs (8-8) was tagged for seven runs and 10 hits in 3 1/3 innings in his first start since coming off the disabled list after being sidelined by a left adductor strain.
"I don't know if he felt that great," Angels manager Mike Scioscia said. "He missed some time with the groin injury. It didn't look like it was very crisp. On a night where obviously we needed some innings out of him, unfortunately he couldn't get to a certain point of the game. He battled hard. He missed some spots, wasn't very crisp and those guys hit the ball well."
A's third baseman Matt Chapman hit a run-scoring single in the first inning to reach base safely in a career-high 25th consecutive game.