Gallardo (6-6) struck out four and walked three while allowing four hits in his 101 pitches. The right-hander has won all three of his decisions over his last five starts.
Odor was recalled from Triple-A Round Rock earlier Monday when outfielder Delino DeShields (left hamstring) was put on the 15-day disabled list with a strained left hamstring.
After singles in his first two at-bats off Carlos Frias (4-4), Odor greeted reliever Adam Liberatore with a two-run single in the sixth that put the Rangers up 4-0.
Shawn Tolleson worked the ninth for his ninth save in as many chances, a day after giving up a ninth-inning run in a tie game that became a 4-3 home loss to Minnesota.
Rangers reliever Tanner Scheppers gave up a long homer to Yasmani Grandal on the first pitch he threw after taking over in the eighth.
The Dodgers still had two on with one out in the eighth when Yasiel Puig struck out for the third time and then snapped the bat over his leg in frustration. Puig also shattered a light in the tunnel leading out of the dugout when he slammed the broken bat there.
Puig also batted with two on in the sixth, and hit a towering flyball to right than Shin-Soo Choo initially couldn't find. Choo recovered, backpedaling with his glove arm extended as far as possible when making the catch. Adrian Gonzalez then grounded into an inning-ending double play.
In the big Texas sixth, Frias walked the first two batters before consecutive RBI singles by Prince Fielder and Mitch Moreland, who has a 10-game hitting streak.
Frias struck out four and walked three while giving up four runs in 5 1-3 innings.
When Odor was sent down five weeks ago, he had hit .144 with 25 strikeouts after starting 25 of the Rangers' first 31 games at second base. The second baseman then hit .355 with five homers in 107 at-bats in 30 games at Round Rock.
Dodgers: RHP Pedro Baez (pectoral muscle) is scheduled to throw live BP on Tuesday and then likely a bullpen session in Los Angeles after that. Manager Don Mattingly said if those go well, "we'll be talking about a rehab assignment for him." ... Mattingly said OF Carl Crawford (right oblique) has "started swinging a little bit."
Rangers: Slugger Josh Hamilton swung a bat for the first time since straining his left hamstring two weeks ago. Hamilton said he felt fine after hitting off a tee and also some soft tosses. ... LHP Martin Perez, pulled from his rehab assignment from Tommy John surgery because of a tweaked left groin, is set to throw a bullpen session Tuesday. ... LHP Matt Harrison (spinal fusion surgery) said he felt good after his latest rehab start, 6 2-3 innings on Sunday for Triple-A Round Rock. He's scheduled to pitch again Friday.
Dodgers: Lefty Brett Anderson has a 2.79 ERA over his last eight starts, but is only 1-3 in that span. He has induced 142 ground balls, leading the majors in ground-ball percentage at 67 percent.
Rangers: Rookie right-hander Chi Chi Gonzalez makes his fourth major league start, having allowed only one in 21 2-3 innings.