McAllister (5-7) yielded two runs (one earned) on four hits while walking one and striking out seven, notching his first win in five starts since returning from a right middle finger injury.
Cleveland was leading 3-1 in the sixth when Raburn homered with Carlos Santana aboard to ice the victory.
Twins starter Samuel Deduno (7-6) was tagged with the loss, surrendering five runs (four earned) on five hits in a six-inning effort.
Josh Willingham pounded a solo homer for Minnesota.
Swim Week Miami Beach 2014 [PHOTOS]