The Twins put together a five-run sixth inning to close within one, but they wound up being swept by the Red Sox while losing their fifth in a row.
Aviles highlighted a four-run second inning with his fourth homer of the year and Jarrod Saltalamacchia contributed a two-run single in the third. Adrian Gonzalez tacked on a run-scoring single in the fifth, which wound up being the winning run when Minnesota made its comeback bid in the sixth.
Minnesota's five-run inning was highlighted by a two-run single from Joe Mauer.
Clay Buchholz (2-1) got the win despite giving up five runs on 10 hits over 5 1/3 innings.
Liam Hendriks (0-1) allowed seven runs on nine hits in four-plus innings to take the loss.
Minnesota's Chris Parmelee left the game after being hit in the bill of the helmet by a pitch thrown by Justin Thomas. Parmelee was able to leave the field under his own power.
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