The rookie slugger and his teammates are both seeing rewards for their persistence heading into the final weeks of the playoff chase.
Myers had never faced Weaver, but he homered on the first pitch he saw from the Angels' longtime ace in the second inning. He homered again in the seventh on Weaver's first pitch after a mound visit, driving a two-run shot into the Rays' bullpen behind left field.
"The only way to get through a slump is to keep hitting," said Myers, who batted just .209 in August after an impressive start to his major league career. "You can't take days off. It's good to be able to help the team like that. Definitely a nice feeling."
Tampa Bay (77-61) stayed 2 1/2 games ahead of the Yankees atop the wild-card standings and remained 5 1/2 games behind first-place Boston in the AL East.
"We don't want just a wild card," Myers said. "We're still trying to win the division. It's nice to not be looking from the outside (at) the wild card, but we still want more than that."
Myers is bouncing back from a rough stretch in August to stay in contention for the AL rookie of the year award alongside teammate Chris Archer, Texas' Martin Perez and Angels leadoff hitter J.B. Shuck. Myers, who didn't get called up to the majors until June 18, had his first multihit game in two weeks during Tampa Bay's win Tuesday night.
Weaver (9-8) yielded six hits over seven innings, giving up two no-doubt shots to Myers, who hadn't homered since Aug. 14.
"He's got some pop, obviously," Weaver said. "There's some holes there, but I didn't quite find those holes. Just two bad pitches ended up beating us, but I felt like I threw a good game for the most part. I threw up a quality start, which (was) the only thing I could do. It's tough."
Myers' first homer off Weaver also produced his first RBI since Aug. 20. He finished with his second multihomer game of the season, having also done it July 28 at Yankee Stadium.
"Those balls were crushed," Tampa Bay manager Joe Maddon said. "That's nice to see. We could really use that right about now. This is a young man that's not overwhelmed. He's going to have some moments, but that's a Cy Young-caliber pitcher, and he handled it well."
Myers provided all the offense needed by Jeremy Hellickson (11-8), who pitched scoreless ball into the sixth inning of his first victory in nearly six weeks. Hellickson yielded four hits and two walks in his first start since spending a week in the minors to rediscover his form.
"Sitting at home for those four, five days and watching the guys in the dugout having fun, and I'm sitting on the couch by myself, it isn't too fun," said Hellickson, who never actually pitched in the minors.
The bullpen also was solid for the Rays, who won their second straight after a five-game skid. Fernando Rodney earned his 32nd save in the ninth while making his first appearance in a week for Tampa Bay, which has won two straight after a 1-8 skid.
Hellickson had allowed multiple runs in each of his previous six starts while going 0-5 with a 9.00 ERA, but he mostly avoided trouble from the Angels, who have lost two straight after winning nine of 10.
Chris Iannetta had a pinch-hit homer in the seventh for Los Angeles, which has lost 11 of 13 at home.
"We've been playing some good baseball," Weaver said. "We had some opportunities tonight, but Hellickson made some good pitches and kept us off balance."
Iannetta connected off Jake McGee to lead off the seventh, hitting his third career pinch-hit homer and his first since Sept. 29, 2009. The Angels catcher hadn't homered at home all season, hitting his other seven homers away from the Big A.
Josh Hamilton went 1-for-3 with a walk in his return to the Angels' lineup. The $125 million designated hitter is struggling with sinus congestion.
Iannetta hadn't homered in Anaheim since Aug. 29, 2012. ... Los Angeles allowed multiple stolen bases for the 28th time this season. ... Maddon said nobody showed up at a Long Beach sports bar late Tuesday night to take advantage of his Twitter offer to buy a beer for anybody in Rays gear. Maddon blamed himself for sending out the offer far too late to find any fans. Still, 20 to 25 Rays players, coaches and personnel enjoyed the "Win or Weep" party until well after 1 a.m. Maddon, a former Angels coach, still has a home in the area.