Murphy's blast off Jose Ortega (0-1) erased a 7-5 deficit for the Rangers, who banged out 18 hits in the victory, their third in a four-game series with the Tigers.
Mitch Moreland added two hits and drove in a pair of runs and Geovany Soto went 3-for-5 with a run scored for Texas, which improved to an MLB best 29-15.
Robbie Ross (2-0) earned the victory with a scoreless seventh inning and Joe Nathan wrapped up the win with his 13th save.
Cabrera finished 4-for-4 with a three-run clout and two solo shots in the second three-homer game of his career.
Prince Fielder supplied a bases-clearing double for the Tigers, who fell for the fourth time in five contests overall.
2014: The Year in Music [PHOTOS]