After getting two outs, Hunter walked Torii Hunter before serving up a fastball that Cabrera crushed into the bullpen beyond the wall in left-center. Martinez came up next and stroked a solo shot to make it a 4-1 game.
Cabrera and Martinez both had two hits for the Tigers, who have won three of their last four.
Justin Miller (1-0) earned the win after allowing just one hit in two innings in relief of starter Drew Smyly, who conceded one run on five hits with seven strikeouts over six frames.
Notable deaths of 2014 [PHOTOS]