The 29-year-old right-hander threw 72 of his pitches for strikes and did not walk a batter en route to his second win. He struck out seven before Greg Infante worked the ninth for his third save and a 2-1 win over Mississippi.
The Braves went down in order in each of the first three frames before mounting their lone rally in the fourth. Tyler Pastornicky reached on a one-out error by first baseman Christian Marrero, advanced to third on a passed ball by Josh Phegley and a groundout and then scored on Ernesto Mejia's double to left. Zaleski escaped the frame when he got Donell Linares to bounce out to first.
The Arlington Heights, Ill., native retired the next 12 batters he faced to end his night.
It was the righty's best start since he struck out eight and held Triple-A Rochester to one hit over seven scoreless innings on June 18, 2010. Zaleski never thrown a complete game in pro ball.
The Indiana State product has logged his share of innings in the Minors since being drafted by the White Sox in the 30th round of the 2004 Draft. He spent all of last season with Triple-A Charlotte, where he went 7-8 with a 5.17 ERA in 28 outings, prompting the organization to move him back to the Southern League this spring.
The Barons took an early lead in the first when Andrew Garcia drew a one-out walk and scored on Brandon Short's line drive single to right. Seth Loman singled home Phegley in the bottom of the fourth to regain the lead.
Infante avoided trouble in the ninth after Loman reached on a bad throw by Phegley. He got Willie Cabrera to ground out to short to seal the combined one-hittter.