Kevin Kiermaier added a two-run double for the defending AL champions, who moved back above .500 with their third straight win. Tampa Bay's first four runs were abetted by the Angels' first three errors in a four-error performance by the majors' worst fielding team.
"We'll take anything right now, but it is encouraging to see the guys not take anything for granted and just put pressure on the defense," Tampa Bay manager Kevin Cash said. "You want to be viewed as a team that's constant pressure, and we have the team to do that."
Meadows then hit a solo homer in the seventh inning and a three-run shot in the eighth for his second career multi-homer game, his first since April 2019. He is the first Tampa Bay player with five RBI in a game since August 2019, and he had the Rays' first multi-homer game this season.
Mike Trout hit his eighth homer and José Iglesias drove in two late runs for the Angels, who have lost three in a row and nine of 13 to fall two games below .500 for the first time this year. Los Angeles, which leads the majors with 29 errors in 28 games, hadn't committed four errors in a game since September 2015.
"We haven't been good," Angels manager Joe Maddon said. "We're absolutely better than that. You're talking about three really good defenders making mistakes tonight. I really feel that's going to go away. I want to believe it's an anomaly moment. I know we're better than that."
Shane McClanahan pitched four scoreless innings of two-hit ball for Tampa Bay in his second major league start, throwing only 63 pitches before Luis Patino (1-0) came on for the fifth. McClanahan's 100-mph stuff was still popping, but the Rays have allowed him to go only four innings in each of his first two starts.
"I'm just going to control what I can control," McClanahan said. "They tell me how many I'm going, and I'm going to try to do it. They're doing a good job controlling everything and playing it smart. Ultimately I've just got to trust them."
Tampa Bay scored three unearned runs on the Angels' errors, which sabotaged starter Alex Cobb (1-2).
Cobb struck out eight while yielding two hits and five walks over five innings against his former team, but left trailing 2-0 thanks to the Halos' leaky defense.
"I have a huge amount of faith in this defense," Cobb said after his first home start in a month. "I've seen what they're capable of. It's been odd, just the hops that we're getting. I don't know how to attribute it to anything other than just some funky hops. ... It's going to even out on us. Those guys are too good."
Manuel Margot reached on Iglesias' error in the first inning and scored from first when David Fletcher booted Brandon Lowe's groundball single in shallow right field.
In the fourth, Randy Arozarena singled, stole second, advanced on catcher Max Stassi's wild throw and scored on Meadows' groundout.
Kiermaier's slow-bouncing grounder in the sixth somehow got between two Angels in the drawn-in infield. Kiermaier then hustled to second when right fielder Jared Walsh was slow to throw back to the infield.
Trout connected for a high-arching solo shot off Patino in the sixth, but Meadows homered leading off the seventh for the Rays.
AL MOVES UP
Albert Pujols singled in the seventh for his 3,253rd career hit, breaking his tie with Nap Lajoie for 13th place in baseball history. Pujols is two hits behind Eddie Murray for 12th.
Cobb spent his first six major league seasons with Tampa Bay. A few months after Cobb left for Baltimore in 2018, the Rays drafted McClanahan with a compensatory pick - 31st overall - created by Cobb's departure.
Rays: RHP Michael Wacha went on the 10-day injured list with right hamstring tightness. The Rays activated RHP Collin McHugh, who was out with a back strain.
Angels: 3B Anthony Rendon sat out after bruising his knee with a foul ball Monday night. ... LF Justin Upton left before the sixth inning with a bruised knee, also after fouling a ball off his leg in the fourth.
Rays: Andrew Kittredge (3-0, 1.54 ERA) will make his second start of the season Wednesday as their opener.
Angels: Shohei Ohtani (1-0, 3.29 ERA) makes his fourth mound start of the season after a two-day delay because he got hit on the right elbow by a fastball in Seattle last Sunday. The two-way star is also expected to hit.
Meadows cranks a pair of home runs
Austin Meadows hits two deep balls for the Rays in their win over the Angels.