Miley started Saturday after missing a month with a lat strain. Winker, who hasn't played since May 27 because of a cervical strain, was batting second.
The Brewers are hoping Winker regained his power during his rehabilitation assignment in Nashville.
Winker, 29, averaged 16.5 home runs per season from 2019-22 -- including a career-high 24 with the Cincinnati Reds in 2021 -- but he hadn't gone deep in 39 games with Milwaukee before his neck injury. He was hitting .204 and had only three extra-base hits, all doubles.
He homered three times in seven games with Nashville and had a .500 on-base percentage.
"He had some success and hopefully found something that's going to carry over to some of his duties here," Brewers manager Craig Counsell said.
Miley, 36, had been one of Milwaukee's most reliable starting pitchers before his injury. The left-hander has a 3-2 record and 3.67 ERA in eight starts.
Milwaukee expected Miley to miss six to eight weeks when he was placed on the IL on May 16, but he recovered quickly and needed just one minor league rehab start before returning to the big league club.
"We thought the symptoms would last longer, but they were gone quicker than we thought," Counsell said. "So when he started throwing again, he had no reason to slow down."
Singleton, 31, hit just .103 with a .188 OBP, no homers and two RBI in 11 games. He posted an .867 OPS in 49 games at Nashville, earning him a promotion and enabling him to make his first major league appearance since 2015.
"When you get pitched tough, get squeezed on a couple of calls and miss a couple balls you're supposed to hit, that's what a 30-at-bat sample size looks like," Counsell said. "And with Jesse healthy, we had to make a move.
"I still think Jon can hit big league pitching."
Miller, 27, was 0-0 with a 5.19 ERA in six relief appearances with the Brewers.
The team also announced that right-hander Cam Robinson, who was designated for assignment earlier in the week, cleared waivers and was outrighted to Double-A Biloxi.