Murphy's two-run single highlighted a four-run third inning that put Texas ahead for good, and his solo shot in the fifth put the Rangers up 7-2.
Josh Hamilton and Adrian Beltre preceded Murphy's blast with back-to-back homers in the fifth and rookie Jurickson Profar also went deep in his first major-league game for American League West-leading Texas.
Derek Holland (10-6) yielded a pair of runs on seven hits over seven innings, walking two and striking out six as the Rangers took the rubber match of a three-game series.
Indians starter Zach McAllister (5-6) was pounded for seven runs on 11 hits through five full innings.
Carlos Santana knocked a two-homer for the Tribe.