Marcus Semien's two-run home run, a run-scoring Mitch Garver single and a pivotal ninth-inning Diamondbacks error produced the runs that enabled Texas to win Major League Baseball's best-of-seven final by 4-1.
"It's just emotional," Semien said. "Everything I have ever worked for is for this moment."
Texas went undefeated in 11 contests on the road away from their suburban Dallas home ballpark, capped by sweeping three games in Phoenix over the Diamondbacks.
The D-backs suffered their first World Series defeat, having won the 2001 crown in their only prior appearance.
Arizona pitcher Zac Gallen kept Texas hitless through six innings, the 28-year-old US right-hander baffling the same batters who blasted out 11 runs on 11 hits the night before.
But the Rangers pounced for a run on three hits in the seventh inning and scored four more in the ninth to secure the crown.