The Rangers remained tied with Oakland at the top of the American League West by winning their fifth in a row and for the 10th time in 11 games.
Texas had to overcome a 4-2 deficit and did so by scoring seven times over the final three innings.
Jurickson Profar brought the Rangers within one with an RBI single in the seventh and Texas then struck for four in the eighth to take control.
Adrian Beltre singled in the tying run in the eighth and Texas then loaded the bases with two out before Profar drew a bases-loaded walk that put the Rangers in front. Martin followed with his key double that gave Texas a 7-4 advantage.
Matt Garza (2-1) gave up four runs over seven innings, but hung around long enough to escape with the win.
The go-ahead run in the eighth was charged to Josh Zeid (0-1). It was his first major league decision in six relief appearances.