Tigers manager Jim Leyland and pitcher Justin Verlander were ejected in the bottom of the fourth inning, when the Tigers apparently thought starter Chad Durbin didn't get a strike call while pitching to Travis Hafner.
After Hafner struck out, Leyland raced onto the field to argue with home plate umpire Tony Randazzo and was quickly ejected. While that was going on, second base umpire Greg Gibson ejected Verlander, who was yelling from the dugout.
"There's no panic on this team," said Leyland, whose club had lost six of seven going into the game. "We know we have a good team. We finally got one."
Ordonez had his second four-hit game of the year, highlighted by a two-run homer in the third.
"We got some big hits," Rodriguez said. "We got some rallies together."
Durbin (5-1) allowed five runs in 5 1/3 innings. He hasn't lost since his first start of the season against Baltimore on April 9, a span of 10 starts. The right-hander allowed eight hits, walked three and struck out one.
"The significant thing is beating the Indians," Durbin said. "They have a good team. It will be a battle all year. It will be a heavyweight fight."
The winning rally started when Ordonez doubled to lead off the fifth. Rodriguez drove him in with a double to right-center off starter Cliff Lee (2-3).
Lee allowed five runs and eight hits in 4 1/3 innings. He struck out four and walked three.
"I pitched bad again," said Lee, who is 0-3 and has allowed 16 earned runs in 13 1/3 innings in that stretch. "That's pretty much it. I keep getting ripped. We're too good of a team for me to be pitching like this."
Ordonez's two-run homer off Lee in the third broke a 1-1 tie and highlighted a three-run inning. The rally continued when Marcus Thames doubled off the wall in left and Sean Casey doubled for a 4-1 lead.
Omar Infante singled in runs in the second and sixth.
Hafner had an RBI single in the first.
"We had some chances to get to Durbin," Indians manager Eric Wedge said. "He gave them a great effort. We let him off the hook."
- The ejection was Leyland's second of the season.
- Ordonez has had four hits 16 times in his career.
- Peralta, who also had a throwing error in the fourth, extended his hitting streak to 11 games.
- Both teams wore replica uniforms from the 1970s.