Center fielder Blake Tekotte put the White Sox (8-7-2) on the board with an RBI triple in the third and right fielder Dewayne Wise hit a solo homer off Scott Downs to start the sixth.
Trout, who went 2-for-3 with two RBIs and three runs scored, hit a line-drive homer to left field to start the bottom of the first, then hit one off the very top of the wall to lead off the third, giving him four extra-base hits in his last four at-bats.
"He's a good hitter," Danks said. "That's saying a lot when you stand out in that lineup. You have to just tip your hat. I didn't make two good pitches to him, but he did what good hitters are supposed to do and make me pay for it."
The Angels added a couple more runs that inning, on a double by the red-hot Howie Kendrick and a sacrifice fly by Josh Hamilton, starting his fifth straight game in right field.
The Angels (4-11-3) blew the game open in the fourth, scoring four runs on a double by Hank Conger, a groundout by Trout, a triple by Kendrick and a single by Albert Pujols.
Kendrick, who drove in two runs, and Pujols each went 2-for-3.
Pujols isn't slated to play first base for at least another week, but he started and ran for himself for a second straight day -- though he came out of the game upon reaching first base after his third plate appearance in the fourth. Pujols is 6-for-14 (a .429 batting average) this spring.
Vargas bounced back after giving up four runs in three innings against the Rockies his last time out, scattering a pair of hits, striking out five and finding success with his off-speed pitches.
"To be able to go out and have that secondary stuff work, and get swings and misses, it's always a good indication of them not being able to stay on your fastball," Vargas said. "For me, that's a good sign."
J.B. Shuck added a two-run single in a four-run seventh inning for the Angels for a 12-2 lead.
Up Next for the White Sox: It's the second and final Cactus League meeting between Chicago's crosstown rivals, as the Cubs make their way from Mesa to take on the White Sox at Camelback Ranch. Gavin Floyd gets the start for the White Sox in a game that will be broadcast on WGN-TV and WSCR 670 AM, the team's flagship radio station. It has a special start time of 2:05 p.m. CT.