"One constant is we've been getting good consistent starting pitching," Los Angeles manager Mike Scioscia said.
Maybin led off by homering on a 3-1 pitch from Alex Cobb. Trout connected on the next pitch for his 15th homer, including seven in his last 11 games.
Shoemaker (4-2), coming off victories over Detroit and the Chicago White Sox, gave up three hits, three walks and struck out five in 6 1/3 innings. He has won all four career starts against the Rays.
Los Angeles has won seven of nine. The Rays have lost three in a row after a season-high four-game winning streak.
Since getting two homers and three hits in the first Monday, Tampa Bay has seven hits over 17 scoreless innings.
"Well, the bats have kind of gone quiet," Rays manager Kevin Cash said. "We'll get out of this. Wouldn't be surprised if we really turn it on (Wednesday night)."
Cobb (4-4) allowed four runs and seven hits over 7 1/3 innings.
"This one is difficult for me," Cobb said. "One of the more frustrating games. We lost the ballgame. (I) got beat without being aggressive early on."
Trout has a hit in 25 of his last 29 games, and has reached base in 40 of his 42 games this season. He moved past Troy Glaus into sole possession of fourth place on the Angels' career home run list with 183.
Shoemaker had allowed just a bunt single and a pair of walks until Logan Morrison had a one-out double in the seventh. After Tim Beckham walked, Colby Rasmus hit a single off the right field wall that loaded the bases.
"Obviously, that was huge that ball stayed in the park," Shoemaker said.
Yusmeiro Petit replaced Shoemaker and worked out of the jam by striking out both Steven Souza Jr. and Derek Norris. Petit and Jose Alvarez, who entered with one out in the eighth, combined to strike out all five batters they faced.
"Petit's been as important as any piece on our pitching staff," Scioscia said.
Keynan Middleton pitched the ninth to complete a three-hitter.
Luis Valbuena had an RBI single in a two-run eighth.
Angels: DH Albert Pujols singled in four at-bats and is 1 for 7 after missing three games with right hamstring soreness.
Rays: C Wilson Ramos (right knee surgery) threw to the bases for the first time and could be ready for a minor league rehab assignment in the next week. "Feeling really close," said Ramos, who was an NL All-Star last year with Washington. He has been hitting and catching bullpens. ... 2B Brad Miller (abdominal strain) took grounders but hasn't started running. ... RHP Tommy Hunter (strained right calf) allowed two runs, three hits and struck out three over one inning in his first game with Class A Charlotte.
Trout is 5 for 9 lifetime with two homers off Cobb. He has 10 homers in 122 at-bats against Tampa Bay pitching.
Only twice previously have the Angels started a game with consecutive homers, coming on Aug. 6, 2013, against Texas (Kole Calhoun and Trout) and May 21, 1996 (Rex Hudler and Don Slaught) at Baltimore.