The Tigers came into the second half of the season with the longest active winning streak in the majors and extended it to six games.
Baltimore starter Jason Hammel (8-6) left the game in the fourth inning with what team officials said was an injury to his right knee. He suffered the injury while throwing to the first batter in the inning and wound up taking his fourth loss in as many starts.
With the Tigers already owning a 3-1 lead heading into the fifth, Cabrera hit a one-out homer off Luis Ayala.
Boesch had a two-run single in the first and Ryan Raburn doubled home another Detroit run in the fourth.
The win went to Doug Fister (3-6), who allowed a run on just three hits with eight strikeouts in seven innings.
This was Fister's 12th start of the season and he has won his last two after spending the early portion of the season on the disabled list.