Rangers shortstop Elvis Andrus said the key with Richards is "You don't know what's coming. He can sink. He can cut the ball. He's controlling his breaking pitch the way he wants to, to keep the ball down."
Albert Pujols and Erick Aybar had two hits each for Los Angeles, and Alex Rios had two for Texas.
Rangers right-hander Nick Tepesch (3-5) retired the first 10 batters he faced before Trout sent a 1-0 sinker 418 feet to center field for the game's first run. Tepesch allowed two runs in the seventh.
The Rangers left eight men on base and went 0 for 6 with runners in scoring position, each of the latter coming with two outs.
The Angels have won eight of their last nine games and 17 of their last 21. Their record of 24-9 since June 6 is the best in the majors during that span.
"The team chemistry is unbelievable," Trout said. "We have to keep thinking one game at a time. We can't look too far ahead."
Tonight's win doubles club victory total here from a year ago (1-9). #Angels
The Rangers (38-55) have lost 12 of their last 13 games and 20 of their last 23, saddling them with the worst record in the major leagues.
Texas manager Ron Washington delivered a passionate, 30-minute talk to his players after their 15-6 loss to Los Angeles on Thursday night and said he saw progress from his team in Friday's defeat.
"We played a much crisper game," Washington said. "It's tough when you have to face a guy like Richards."
Pujols opened the Angels' seventh with a shot that went under Andrus' glove and was ruled a single. Josh Hamilton pulled a liner to the right side that skimmed off the glove of second baseman Rougned Odor, sending Pujols to third.
Aybar hit an opposite-field flare to left that scored Pujols and ended Tepesch's night. David Freese greeted reliever Neftali Feliz with a single up the middle to score Hamilton.
Rangers third baseman Adrian Beltre, one of the club's two All-Stars, extended his hitting streak to 15 games with a third-inning single.
NOTES: The Rangers signed RHP Jerome Williams, released by Houston in June, to a minor league contract and assigned him to Triple-A Round Rock. Williams was 1-4 with a 6.04 ERA in 26 appearances. ... Angels RHP Jared Weaver said he will be ready to start Saturday after leaving Monday's game after two innings with a stiff back. ... Rangers C Geovany Soto made a written apology through the club after being arrested Wednesday on a misdemeanor charge of marijuana possession.