With the score tied 4-4, Kevin Youklis drew a one-out walk from Mike Moore (0-1) and Ortiz followed by drilling a pitch off the center field wall as Youklis slid home safely.
Mike Aviles added a solo homer in the next frame to insure the victory for the Red Sox, who also got a three-run blast from Cody Ross en route to their third straight win over the Rays.
Moore, making his first start of the season, was lit up for six runs on eight hits over 6 1/3 innings.
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