"I saw him throw the curveball a couple times, and I saw that he didn't have a feel for that," Hunter said. "This guy has great stuff -- his changeup, his arm action is the same as the fastball, coming out of his arm. Just the fact that we were able to capitalize on his mistakes - we have a professional team over here. They make the adjustments and battle at the plate."
Fielder also hit a two-run single that capped a four-run second inning for the Tigers. Moore got only six outs while allowing six runs, seven hits and six walks.
Moore (8-1) was pitching on three days' rest after his previous start in Cleveland was limited to one inning because of rain.
"In the second inning, I just lost my release point. That's happened before, and I've got a couple tricks that I can use to get it back, but nothing worked today," Moore said. "I wasn't throwing anything close enough to the strike zone to make them swing at anything."
Anibal Sanchez (6-5) allowed a run and four hits in seven innings. He struck out nine with one walk.
Omar Infante homered and had three RBIs for Detroit, which won for the second time in seven games. It was Tampa Bay's second loss in nine.
Fielder and Jhonny Peralta had three hits each for the Tigers.
The Rays got a run in the second to open the scoring, but Moore immediately allowed a single to Peralta and an RBI double to Matt Tuiasosopo in the bottom half. Infante made it 2-1 with a sacrifice fly, and after two-out walks to Hunter and Miguel Cabrera, Fielder singled with the bases loaded.
"It was a great night," Tuiasosopo said. "He has some great secondary pitches - a great changeup and curveball - so we really wanted to just get after his fastball and not miss that when he threw it."
The third inning wasn't any better for Moore. After a leadoff double by Peralta, he walked two straight hitters and then allowed an RBI single by Avisail Garcia. Moore was finally pulled after he walked Infante to force in a run and make it 6-1.
Alex Torres came on with the bases loaded and nobody out, but he prevented any further damage by striking out Cabrera and Fielder to end the inning.
Moore had allowed only 15 runs all season coming into the game.
Sanchez, meanwhile, has also been impressive this year - although he doesn't have Moore's flashy won-loss record. Sanchez struck out 17 batters against Atlanta in April, and he had a no-hitter broken up in the ninth inning against Minnesota on May 24.
After that 130-pitch outing, Sanchez was knocked around a bit in a loss at Pittsburgh last week. He had an extra day of rest before facing the Rays and looked sharp from the start.
"No matter how many runs we score ... I don't want to allow any runs," Sanchez said. "If we make a lot of runs, the other team can do it, too, so we have to keep the same game."
Infante's solo homer made it 7-1 in the fifth. The following inning, Cabrera went from first to third on a wild pitch when catcher Jose Molina was slow to come up with the ball back by the screen. Molina had his left arm checked after the play but stayed in the game.
Fielder drove in Cabrera with a sacrifice fly, and his 12th homer of the season - a solo shot in the eighth - made it 9-1. Don Kelly added an RBI single later in the inning.
- Tampa Bay announced after the game it had agreed to a minor league deal with C Jesus Flores.
- Hunter's hitting streak ended at 11 games.
- Detroit RHP Doug Fister (5-2) faces Tampa Bay RHP Alex Cobb (6-2) on Wednesday night.