Ten of Boston's runs came on the long balls, sending the Red Sox to their sixth victory in seven games. Miami has lost 12 out of 14.
Mike Aviles started the onslaught with a three-run homer in the second and Cody Ross contributed a three-run double in the third.
Boston then produced a six-run fourth inning that included the grand slam by Ortiz and a solo shot from Jarrod Saltalamacchia. Will Middlebrooks tacked on a two-run homer in the eighth.
Felix Doubront (8-3) gave up four runs on nine hits in six innings, but was still the easy winner.
Nine of the Boston runs were charged to Ricky Nolasco (6-6) in 3 1/3 innings.