Ortiz drilled a two-run shot in the first inning and Kalish's fourth-inning smash turn the contest into a rout as the Red Sox took the first of a three-game series with the Rays at Fenway Park. Ortiz also added an RBI double.
Victor Martinez drove in a pair of runs and Adrian Belte added a solo shot for the Red Sox.
Jon Lester (16-8) collected the win with six innings of two-run ball, yielding four hits and three walks while striking out 10.
Ray starter Jeff Niemann (10-6) was pounded for six runs on four hits in 1 2/3 innings.
Second-place Tampa Bay dropped 2 1/2 games behind the New York Yankees in the American League East with the setback but maintained a 6 1/2-game lead in the AL wild care chase.