In his third start since returning from the disabled list, Marshall gave up a walk and four hits – the last being a solo home run in the eighth inning.
Marshall got behind in the count 3-1 before trying to force a fastball in down-and-away to Zephyrs catcher Gustavo Molina, who pulled the ball over the left-field wall.
Marshall cruised through the first six innings on just 56 pitches, giving up two hits.
He said he felt strong and wanted to finish the game, but the Cubs have tried easing him back into the rotation by regulating his pitch count. He missed two starts after going on the seven-day disabled list on May 24 with a left hamstring pull.
Cubs ace Carlos Zambrano, meanwhile, is scheduled to undergo an MRI on his right shoulder Friday after leaving Wednesday's game at Tampa Bay with discomfort. Zambrano had been set to start Tuesday against Baltimore.
Marshall, who made 13 relief appearances with Chicago earlier this season and gave up four runs over 8 2/3 innings, said he will be ready if needed.
"I know that I'll be ready if they need me and they make the phone call," said Marshall. "I'm looking forward to my next start, whether it's here or in the big leagues."