Cron, who was recalled from Triple-A Salt Lake City July 7, hit the first pitch from reliever Adam Kolarek for his third home run of the season, a line shot down the right-field line that was caught by a fan in the first row of seats.
Logan Morrison hit his 26th home run of the season, a two-run deep fly, for Tampa Bay.
The Rays did little against Bridwell for six innings, with just four hits and running into outs twice. They got to him in the seventh, Evan Longoria singling and Morrison taking a 2-0 slider into the right-field bleachers.
Bridwell departed after 6 1/3 innings, allowing six hits, two runs, a walk and a career-high eight strikeouts.
Rays starter Chris Archer had an uncharacteristic day, walking three batters in the first two innings and five total in his six innings. It was the most walks he has allowed in a game since Cleveland drew six on May 15. He has allowed three walks or fewer in 17 of his 20 starts this season.
He worked around trouble for four innings before the Angels finally broke through. He started the fifth with two walks, but gathered himself and struck out Kole Calhoun and Mike Trout and had two strikes on Albert Pujols when the veteran poked a single to right field to give the Angels a 1-0 lead.
They made it 2-0 in the sixth. Andrelton Simmons doubled, went to third on a fly and scored on Martin Maldonado's bunt in front of the plate. Archer's throw to catcher Jesus Sucre was in time, but the catcher's tag was high on the leg and Simmons' foot slipped under it. Archer finished his day after six innings, allowing five hits with his five walks. He struck out nine.
Morrison's home run evened the game at 2-2. After Simmons singled to start the eighth with his third hit of the day, Cron pinch-hit for Luis Valbuena and went opposite field for the home run and 4-2 lead.
The Rays used three hits in the ninth against closer Bud Norris to close the margin to a run. A Longoria double and singles by Morrison and Steven Souza Jr. made it 4-3. Norris walked Brad Miller to load the bases, but induced Tim Beckham to hit into a game-ending double play.
NOTES: RHP Parker Bridwell was recalled from Triple-A Salt Lake City to start Sunday's game. His demotion was a personnel maneuver to work around the All-Star break and he didn't make an appearance with the Bees. ... The Angels designated 2B Danny Espinosa for assignment. Acquired from Washington in an off-season trade, Espinosa hit .162 in 77 games, with six home runs, 29 RBIs and 91 strikeouts in 228 at-bats. The Angeles will platoon Nick Franklin and Cliff Pennington at second base. ... Rays C Wilson Ramos sat out his second game after suffering a slight strain in his hamstring in Friday's win against the Angels. ... INF Tim Beckham returned to the starting lineup after being activated from the disabled list. He was out with an ankle injury... Rays 3B Evan Longoria extended his hitting streak to nine games and OF Steven Souza Jr. extended his streak to 12 games.