The score was tied 1-1 in the fourth when the Tigers exploded for eight runs, including back-to-back-back solo shots in addition to Cabrera's slam.
T.J. McFarland relieved but the Tigers' onslaught continued as Avisail Garcia singled and Omar Infante followed with an RBI double for a 5-1 lead.
Andy Dirks drew a walk to load the bases and Cabrera then belted a 3-2 pitch into the left-field stands for his 17th round-tripper of the season.
Tuiasosopo went 2-for-3 with a fifth homer for Detroit as the Tigers broke a four-game skid.
Justin Verlander (7-3) notched the victory, yielding three runs on eight hits over seven innings. The Tigers ace walked one and struck out five.
Hammel (7-3) was lit up for five runs on five hits over three full innings.
J.J. Hardy pounded two solo homers for the Orioles.