Calhoun pulled a 2-0 pitch from Nick Ramirez just inside the right-field line and into the corner. Calhoun later scored on a wild pitch.
José Cisnero (0-3) walked the first two batters of the seventh and was replaced by Ramirez with two outs.
Rafael Montero (1-0) closed with 2 1/3 scoreless innings for his first major league win since September 2017 with the New York Mets. Texas’ four-game win streak is its longest since a six-game streak in late June.
The Tigers went 2-8 on a 10-game road trip.
Detroit right-hander Jordan Zimmermann permitted four runs and six hits in six innings. He was trying to win for the second straight time after going 0-8 in his first 13 starts of the season.
Zimmermann had retired eight straight batters and was working with a 3-2 lead with one out in the fifth when Shin-Soo Choo hit a liner back to the mound. Zimmermann spun to his left and dropped to the dirt as the ball skimmed off the top of his glove for a hit. The next batter was Danny Santana, who hit a 2-2 slider into the seats in right.
Texas rookie Pedro Payano allowed three runs, two earned, and six hits in 4 1/3 innings in his second career start.
Rangers right-hander Emmanuel Clase pitched 1 2/3 innings of no-hit relief in an impressive major league debut. Clase struck out one and walked one. Ten of his 25 pitches hit double digits according to MLB.com, topped by 101.1.
Clase’s contract was selected from Double-A Frisco on Friday. He had a combined 50 strikeouts in 44 2/3 innings this season with Frisco and High-A Down East.
FOUL BALL INJURY
A female fan seated in the 25th row down the right-field line was struck in the head by a liner hit by Calhoun. He waited for a few minutes and watched as the fan was attended to at her seat before returning to the batter’s box. The fan eventually walked out of the seating area accompanied by stadium personnel and was transported to a hospital for further evaluation.
Tigers: INF Josh Harrison (hamstring), out since Memorial Day, played his fourth rehab game for Triple-A Toledo. He went 2 for 3 with two RBIs and a walk after previously going 0 for 9.
The Tigers haven’t announced a starter for Monday in the first of three games at home against the Chicago White Sox. Rangers left-hander Mike Minor (9-6, 3.21 ERA) will open a three-game series at Cleveland, having held the Indians to one run in eight innings in a win on June 20 in Arlington.