Rogers (12-6), who was 0-3 in his previous six starts, allowed two runs and five hits. He struck out one and walked four. Ivan Rodriguez also had three hits for the Tigers.
"It was nice to get a win for myself," Rogers said. "But more important was the win for the team."
Rogers left with the bases loaded and none out in the sixth. Zumaya relieved him and walked Mark DeRosa to make it 4-2. But Zumaya then got Ian Kinsler to foul out and struck out Hank Blalock and Gerald Laird to end the inning.
After the walk to DeRosa, Zumaya's first pitch to Kinsler was a ball. Pitching coach Chuck Hernandez then came out to talk to the rookie and he immediately began throwing strikes.
"I was a little jumpy on that first batter," Zumaya said. "... After Hernandez came out, it calmed me down. He can tell when I need talking to."
Not only was Zumaya getting his fastball over, which can reach triple digits, but he got his changeup in the strike zone, too.
"When you can get your offspeed pitches over and can throw 100 miles per hour," Laird said. "You're going to be pretty tough."
Detroit's bullpen retired 11 of the last 12 batters. Blalock's single off Jones with one out in the ninth broke a string of 10 consecutive Rangers set down. Laird then grounded back to Jones for a double play to end the game.
"The bullpen really picked me up," Rogers said. "They did a little extra work for me tonight."
Edinson Volquez (1-2) only lasted 3 2-3 innings for the Rangers. He allowed three runs and eight hits, struck out one and walked three. He left the game with the bases loaded and two out in the fourth. Joaquin Benoit then came on and fanned Dmitri Young to end the threat.
"I've got some problems with my mechanics," Volquez said. "My front side was a little open."
Guillen singled with one out and moved to third on a hit-and-run single by Rodriguez. Casey then followed with a soft liner that dropped into right-center to score Guillen and send Rodriguez to second. After a fielder's choice by Brandon Inge moved Rodriguez to third, Infante singled to left.
Young singled in a run in the third but the Rangers scored without the aid of a hit in the fourth to pull within 3-1.
Rogers walked leadoff batter Mark Teixeira, who moved to second on a wild pitch. A groundout sent Teixeira to third and he came home on Kinsler's slow roller to first.
Guillen hit a one-out solo homer off Benoit in the fourth. It was his 14th of the season.
"I wasn't trying to hit a home run, but I hit it pretty good and it went out," Guillen said. "It proved to be pretty important."
The Rangers were short-handed after manager Buck Showalter and pitchers Vicente Padilla and Scott Feldman were suspended for their role in Wednesday night's on-field altercation with the Los Angeles Angels.
Showalter was handed a four-game suspension, which began with Thursday night's game. Padilla will sit for five games, also starting Thursday, and Feldman received a six-game suspension, which will start when Padilla returns. Bench coach Don Wakamatsu is managing in Showalter's absence.
- Detroit backup C Vance Wilson signed a two-year contract extension worth $1.9 million.
- Casey has driven in nine runs in his last nine games and 13 in 16 games with Detroit since being acquired from Pittsburgh.
- Tigers 2B Placido Polanco will miss four-to-six weeks with a third-to-fourth degree shoulder separation. He suffered the injury Tuesday night in Boston.