Price (3-1) tamed the Angels on five hits, issuing only one walk while striking out six en route to his second career shutout and first since 2010.
The left-hander allowed only one runner to reach as far as third base and tossed 80 of his 119 pitches for strikes in the dominating performance, which handed the Rays a win in the opener of a three-game set.
The Angels' Ervin Santana (0-4) lost a fourth straight start to start the season, allowing five runs on eight hits over five frames.
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