Johnson's first blast came in the second inning, capping a six-run Rays outburst, and his second iced the win as Tampa Bay was clinging to a one-run lead in the eighth.
The Rays' bullpen racked up six shutout innings after starter Jake Odorizzi was lit up for six runs over four innings.
Jake McGee (2-2) earned the decision with two frames of scoreless relief as the Rays took the first game in a home-and-home interleague rivalry series.
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