Since giving up a single to the Angels' Vernon Wells on April 12, opponents are 0-for-31 with 11 strikeouts and two walks against Burton.
"It's exciting," Gardenhire said. "We talked about in Spring Training how our bullpen would go and we liked what we saw from him in Spring Training. He's coming off this [shoulder] thing and his pitches are getting better and better. We're not afraid to use him back to back, but we're trying not to. Same with multiple innings. I think that's gonna help him."
Burton, who had arthroscopic shoulder surgery while with the Reds last season, has pitched in consecutive games twice this season, and has yet to throw more than one inning.
He's seen success with a pitch he describes as a "splangeup," which is a combination of a splitter and changeup.
"You definitely see it dive," Gardenhire said. "He throws it with the same arm action as a fastball, so that's the big thing. It throws off the hitter's timing."