The Tigers batted around in the opening inning and the first six men to the plate all reached base against Justin Grimm (7-7).
Martinez also doubled home a run while Detroit was scoring twice in the second.
Doug Fister (7-5) worked six innings for the victory, giving up two runs on eight hits with five strikeouts. It was only his second win in 11 starts.
Texas lost its third straight.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged