Sabathia (18-7) won 17 games as a rookie in 2001.
With the victory, the surging Indians completed a three-game sweep, and tied Boston for the best overall record in the AL.
With Detroit leading, 2-1 in the bottom of the fifth, Franklin Gutierrez, Jason Michaels, and Asdrubal Cabrera all had RBI hits, putting Cleveland ahead for good.
Casey Blake hit a solo homer and five others had one hit for the Indians, who have built a 7 ½-game lead over Detroit in the AL Central Division.
Sabathia walked one batter and fanned seven, and closer Joe Borowski recorded his 42nd save.
Detroit scored on Ryan Rayburn’s third-inning two-run single.
Carlos Guillen had two hits for the Tigers.
Losing pitcher Nate Robertson (8-12) surrendered four earned runs and six hits in five innings.