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.
The Rays (23-25) have dropped three straight at home, scoring a combined four runs in the defeats.
Los Angeles added another run on a sacrifice fly by Kole Calhoun, so both of Cobb's runners scored as Tampa Bay's bullpen woes continued for a second straight night.
Stats: Trout is hitting.347 (52 for 150) with 15 home runs, 35 RBIs, 34 runs scored and nine stolen bases on 10 attempts in 43 games.
"We talked about bouncing back and it was good to see the guys come back after two quiet nights", Rays manager Kevin Cash said. "We are a good team and we will get out of this". "Wouldn't be surprised if we really turn it on (Wednesday night)". Meyer comes off a 7-5 loss at the Mets with four runs (three earned) given up on three hits and four BB over four frames.
"It's kind of hard to go out there in the first and put your team behind that quickly", Cobb said. We lost the ballgame.
Hunter had missed the Rays last 30 games with a right calf strain sustained against the Houston Astros back in April when he attempted to cover first base. He moved past Troy Glaus into sole possession of fourth place on the Angels' career home run list with 183. He allowed just four hits while striking out two and walking one. Rasmus led off the seventh with another home run and Souza, who came into the game in an 8-for-67 slump, followed with his second of the game and seventh of the season.
Petit and Jose Alvarez combined to get all five of their outs on strikeouts, and Keynan Middleton pitched a ideal ninth to close out the win. Runners had to hold up for a potential catch, so it was only a single, loading the bases with one out.
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. The homers by Colby Rasmus and Steven Souza, who had earlier hit a two-run homer, turned a 3-2 game into a 5-2 game.
Tampa Bay Rays relief pitcher Jose Alvarado during the seventh inning of a baseball game against the Los Angeles Angels Wednesday, May 24, 2017, in St. Petersburg, Fla.
Only twice previously have the Angels started a game with consecutive homers, coming on August 6, 2013, against Texas (Kole Calhoun and Trout) and May 21, 1996 (Rex Hudler and Don Slaught) at Baltimore. Matt Andriese (4-1, 3.75 ERA) will take the mound for the Rays.