"That's what you ask for, right? That's what you work for," said Mendick, whose home run landed in the home bullpen. He planned to give the baseball to his parents.
Mendick, who made his major league debut Tuesday, hit a solo shot in the fifth to give the White Sox a 3-1 lead. He started in place of Anderson, who began the day leading the AL with a .334 average.
"It wasn't the easiest road," Mendick said of his career. "I wasn't a first-rounder, didn't have a big name. Being able to do it, I think everyone really likes it and enjoys to see it."
Josh Osich (2-0) threw 2 2/3 scoreless innings to pick up the victory. He combined with two other relievers to limit the Angels to one hit in 5 2/3 shutout innings. Right fielder Cordell fell into the net making a catch in the ninth.
Los Angeles used six relievers.
Abreu hit a solo homer an estimated 462 feet to put the White Sox ahead in the third. His career-high 112 RBI lead the AL.
Jaime Barria (4-8) allowed both home runs in 4 1/3 innings for the Angels and hasn't won since July 24.
Shohei Ohtani singled to drive in the Angels' run in the first. He is 12 for 28 with nine RBI in seven games against the White Sox this season. He went 1 for 4 with three strikeouts after going 3 for 5 with a career-high five RBI on Saturday.
McCann's RBI single tied it at 1 in the first. Opener Noe Ramirez recorded just two outs.
The Angels left the bases loaded in the first and second innings.
Dylan Cease allowed a run and struck out four but walked five and threw 88 pitches in 3 1/3 innings for the White Sox, who had lost nine of 11.
"We certainly had our chances against Cease early on," Angels manager Brad Ausmus said.
Mendick said his teammates were excited for his first homer after pranking him Thursday, when he got his first major league hit, a single, at Cleveland.
"They threw the fake ball in the stands when I got my first hit, so they were like, `We'll take it easy this time,' " he said.
Hermosillo, a rookie recalled from Triple-A Salt Lake a week ago, recorded his first career multihit game.
Angels: Trout (right toe soreness) was scratched from the lineup and is listed as day to day. He was available to pinch hit. "There really wasn't a ton of improvement overnight," Ausmus said. "For some reason, sometimes he can come back the next day and it feels fine and other times it takes a little longer for the soreness to get out of there." ... OF Justin Upton (calf tightness) was held out of the lineup due to the rainy conditions. ... INF Tommy La Stella (broken right tibia) still has soreness in his leg. La Stella has been taking live batting practice, fielding groundballs and throwing. The Angels have no timetable for his return. ... C Max Stassi (side) sat out the series and will get evaluated when the Angels return home Monday.
White Sox: Manager Rick Renteria (shoulder surgery) is expected to return Tuesday. Bench coach Joe McEwing said Renteria will not throw batting practice because his arm is in a sling.
White Sox: After a day off, RHP Ivan Nova (9-12, 4.69) is scheduled to start against visiting Kansas City and RHP Jakob Junis (9-12, 4.94) on Tuesday. Nova is 5-3 with a 2.40 ERA in his last nine starts.
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