Greinke struck out two and gave up just the one hit.
Buehrle looked in midseason form, both in effectiveness and through the quick pace with which he worked. The southpaw induced four ground balls among his six outs, fanning one.
"Actually, I felt really good for early in the spring," Buehrle said. "It's only two innings, but physically, location, everything was there. I say it every spring, but I hope I feel this good Opening Day."
Phil Humber followed Buehrle by allowing one run in two innings, making his push for the seventh and final slot out of the White Sox bullpen.
Milwaukee scored in the third with two outs. Wil Nieves singled, swiped second and came home on Rickie Weeks' single. Singles from Mark Kotsay, who was with the White Sox in 2010, and Yuniesky Betancourt started the fourth against Humber, but he pitched out of the jam without allowing any runs.
Brandon Boggs' two-out, two-run single in the eighth made it a 3-0 game.
Alejandro De Aza's ninth-inning RBI groundout got the Sox on the board.
Milledge reached base via a single and was hit by a pitch. Omar Vizquel and Craig Counsell, the teams' respective elder statesmen, both made slick plays defensively to cut short rallies, while converted right fielder Viciedo threw out Edwin Maysonet trying to go from first to third on a single in the sixth.
Up next for the White Sox: A.J. Pierzynski moves from behind the plate to the designated hitter role on Wednesday, when the White Sox play their first Cactus League game away from home in Goodyear against the Reds. Tyler Flowers takes over at catcher, with the regular starting lineup intact aside from Adam Dunn getting a one-day respite. Edwin Jackson, who is in line to start the second game of the regular season, takes the mound for the White Sox.
Up next for the Brewers: Milwaukee will continue rolling out its string of 2010 Opening Day starters on Wednesday, when right-hander Yovani Gallardo makes his '11 debut against the rival Cubs at Maryvale Baseball Park. Somebody is bound to be disappointed, considering that Gallardo, Zack Greinke and Shaun Marcum all started season openers for their clubs last season, but manager Ron Roenicke has yet to announce his plan. "I imagine it will come pretty soon," Roenicke told reporters Tuesday morning.