Aviles socked a solo homer, Ortiz added a two-run shot and Adrian Gonzalez went 3-for-3 with two RBI and two runs scored for Boston, which clinched its three-game series against the Twins.
Josh Beckett (2-2) earned the decision despite allowing five hits and three walks over six innings. He struck out five as the Red Sox logged their second straight win following a five-game skid.
The Twins' Nick Blackburn (0-2) was tagged for five runs on eight hits in a three-inning start.
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