Santana, who is eligible to return from his 80-game suspension on July 4, went 5 2/3 innings, allowing one run on five hits and two walks. He also struck out three and threw 88 pitches with 53 going for strikes.
"He was rusty, but he threw 88 pitches," Twins general manager Terry Ryan said. "He used all his stuff. They won the game. I think it was good opening for him. Now it's up with competition that's legit.
"All in all, I think it was a favorable line. And now we'll get him up to 100 pitches in his next outing in five days and gear him up for his return. He's right on schedule and hasn't had any setbacks, which is exactly what you hoped would happen."
Santana, who was previously pitching in extended spring training, is scheduled to make two more starts with Rochester, which would line him up for a return with the Twins on July 5 in Kansas City. He gets a 16-day rehab assignment to get ready for his return, according to the terms of his suspension. But he's not eligible to pitch in the postseason.
Ryan also said it's too early to say who Santana will replace in the rotation, as the Twins aren't looking to go with a six-man rotation. Minnesota entered Sunday with a 3.85 ERA from its starting pitchers, which ranks as the ninth-best mark in the Majors this season.
"We have a good problem on our hands," Ryan said. "Our guys have been pitching well. And I don't think it's a mistake, either. Competition brings that out."
• Outfielder Aaron Hicks, on the 15-day disabled list with a strained right forearm since June 14, had an MRI exam on his right forearm, but it came back favorable, according to Ryan. Ryan said Hicks has been playing catch and taking swings during soft-toss drills, and the Twins are hopeful he'll be healthy once his 15 days are up.
• Double-A Chattanooga right-hander Alex Wimmers was named the Twins Minor League Player of the Week. He made two starts, tossing 14 2/3 scoreless innings with 20 strikeouts and four walks.