Leading 3-0 in the fifth inning, Nelson Cruz launched his 35th homer of the season over the center-field wall.
Luis Arraez, who doubled off the Green Monster earlier in the game, reached on a single and scored on Miguel Sano's prodigious blast that landed above the crowd where the TV cameras sit below the scoreboard in center field. Statcast measured the tape-measure shot at 452 feet.
Sano's shot – his 27th of the season – gave the Twins a 6-0 lead before Boston scored four runs in the bottom of the fifth, highlighted by a three-run homer by AL MVP candidate Rafael Devers.
Andrew Benintendi hit a solo homer off Taylor Rogers in the eighth to cut the lead to 6-5,
It was a bullpen game for Minnesota's pitching staff because Jose Berrios had his scheduled start pushed back to Wednesday. Randy Dobnak pitched a clean first inning and Lewis Thorpe was cruising through 3.1 innings before serving up the homer to Devers.
Trevor May, Tyler Duffey, Sam Dyson and Rogers finished the game, allowing a combined two runs on four hits while striking out six over 4.2 innings.
Meanwhile, Cleveland blew a late lead and lost 6-5 to the White Sox. The Twins' win coupled with Cleveland's loss gives Minnesota a 6.5-game lead in the AL Central.
Up next: Twins at Red Sox, Wednesday at 6:10 p.m.