Trailing 8-0 after three innings, the Rays struck for seven runs in the fifth inning in a rally capped by Evan Longoria's two-run homer.
In the next frame, Ryan Roberts hit a one-out double, went to third on a passed ball and scored on a Jose Lobaton sacrifice fly to tie it up.
Then in the eighth, Jeff Keppinger collected a leadoff single against Kevin Jepsen (2-2) and Pena, batting for Sean Rodriguez, followed by belting a 2-2 pitch into the right field stands for the decisive blow.
Ben Zobrist drove in three runs for the American League wild card-leading Rays, who won for the 15th time in 20 games and improved to 8-1 against the Angels this season.
Jake McGee (4-2) earned the win and Fernando Rodney racked up his MLB-best 38th save for the victors.
Mike Trout went 3-for-4 with solo homer and three RBI, while Albert Pujols added a two-run shot for Los Angeles.