After taking two strikes and fouling off three pitches against Rockies closer John Axford, Odor worked his way back to a full count and drew a leadoff walk.
That proved to be the spark needed as the Rangers scored two in the top of the ninth inning and held on for the victory. Elvis Andrus had the big hit of the inning with a two-run single that put the Rangers ahead.
The Rangers led, 8-4, into the bottom of the eighth before reliever Tanner Scheppers gave up four runs on two home runs. Odor's walk helped alleviate the sting of that inning.
"Rougie's at-bat was extremely important," Rangers manager Jeff Banister said. "Down 0-2, he scalded a couple of pitches foul. To be able to grind out the at-bat and draw the walk was huge."
Batting at the top of the Rangers' lineup, Delino DeShields and Odor were a combined 4-for-7 with two walks, a hit batter and seven runs scored.
"A big day for both of those young men at the top of the lineup," Banister said.
Adrian Beltre had three walks in the No. 3 spot, but he followed Odor with a single to right in the ninth, putting runners at first and third. Axford struck out Mitch Moreland, which brought up the pitcher's spot since Banister had used the double-switch to take Josh Hamilton out of the game.
Banister still had Prince Fielder available as a pinch-hitter, but Rockies manager Walt Weiss walked him intentionally to load the bases. That brought up Andrus, and the Rockies still pulled the infield in. But Andrus grounded a single past third baseman Nolan Arenado to drive home two runs.
"Big at-bat by Elvis," Banister said. "He came through in a situation that he has been trying to have success in. He didn't try to get too big. He stayed short and got the ball through the middle."
Shawn Tolleson pitched the ninth inning for his 15th save, preserving a win that was made possible by Odor's patience at the plate.