The AL West-leading Angels' powerful right-hander drilled a pitch from reliever Russ Springer off the right-field foul pole for the decisive blow to give the team an opening victory in a three-game series.
"It came at a time when the team really needed it," Guerrero told reporters.
The blast was also the second home run of the game for Guerrero, who bagged a solo shot in the second inning.
First baseman Kendry Morales also homered twice to reach 25 for the season as Los Angeles (66-44) overcame a determined Rays (61-51) challenge in a game featuring six home runs in total.
Tampa Bay rallied from a 6-3 deficit with three runs in the fifth inning, when Carlos Pena homered to center field to make it 6-6.
After Morales put the Angels back on top with one of his round-trippers in the bottom of the fifth, Jason Bartlett, who finished 3-for-5 with two RBIs, had a game-tying triple against Los Angeles pitcher Jason Bulger in the sixth.
"It just wasn't our day," said Tampa Bay's Ben Zobrist, who finished with two hits.
"They hit a home run off the foul pole. It was a good game. You never like losing, but we hit the ball well today."
Kevin Jepsen recorded the win for Los Angeles after pitching a scoreless seventh and eighth inning, while Brian Fuentes came on in the ninth to pick up his 32nd save of the year.
Young starter Sean O'Sullivan, who pitched a no-hitter in the minor leagues last month, allowed six runs in 4 2/3 innings of a no-decision.
Tampa Bay's Matt Gaza came into the contest having allowed just three runs or less in his last five starts, but was knocked around for six runs in just 3 1/3 innings against the Angels.
