Sean O'Sullivan, a late choice to start with Scott Kazmir getting a few extra days of rest, went five innings and moved to 4-2 with the win.
Brian Fuentes notched his Major League-high 46th save with a perfect ninth after Rafael Rodriguez (two innings) and Jose Arredondo (one) had delivered solid relief.
Regulars Torii Hunter, Kendry Morales, Erick Aybar and Juan Rivera rested, and the others departed mid-game.
O'Sullivan was handed a lead by Bobby Abreu with a solo homer (his 15th) in the first. It came against Texas ace Scott Feldman, who fell to 17-7 with the loss, his first in four starts this season against the Angels.
Jeff Mathis' RBI single made it 2-0 in the second, and Mike Napoli's two-out, two-strike, two-run single made it 4-1 in the fourth after David Murphy had homered in the top half of the inning.
Ian Kinsler doubled and scored on Ivan Rodriguez's groundout to make it 4-2 in the fifth.
"He was getting a little tired toward the end of throwing in our rotation," Scioscia said of O'Sullivan, who had yielded four earned runs in one inning in Toronto on Aug. 21 in his previous start. "He's got the potential to be a terrific Major League starter. He showed good stuff tonight."
O'Sullivan, who gave the Angels a brilliant effort and a win in his Major League debut in San Francisco on June 16, enjoyed ending his season with a victory.
"It's good to end on a better note than what I left in Toronto," O'Sullivan said. "Like I said then, you've got to go through a slump to test your character."
Scioscia emptied his bench in the middle innings and was pleased with the performances of his young players.
"It was good to see these kids get out there and release some energy," Scioscia said. "They've been here for close to a month, and they're tired of those 3 o'clock workouts."
In his first Major League at-bat, outfielder Chris Pettit singled in the seventh inning, later scoring on Howard Kendrick's double. Catcher Bobby Wilson doubled in his second at-bat of the season after lining out to center.
"Chris Pettit had a great at-bat for his first base hit," Scioscia said. "And Bobby Wilson had two very good at-bats."
Starting at shortstop, Brandon Wood doubled and walked, scoring a run. Getting a shot in center field, Reggie Willits had a sparkling defensive play in the sixth on Hank Blalock's liner to leave two runners stranded.
"It's almost like it's more loose playing the game," O'Sullivan said of the mood on the day after the Angels celebrated a third consecutive AL West title. "That's when you play your best baseball -- loose, like when you're a kid. Play hard every time you step on the field. We showed that tonight."
Chone Figgins became the first Angels player with 100 walks since Troy Glaus walked 107 times in 2001. Figgins and Abreu have combined for 195 walks and 208 runs scored, 113 by Figgins.