Hudson allowed one run. He is set to start the opener next Monday at home against Philadelphia.
Venters exited in the sixth after hurting his left elbow in his first appearance since March 13, when he walked four. The lefty was listed as day-to-day.
Juan Francisco hit a go-ahead homer in the ninth off Brayan Villarreal. Ramiro Pena also homered for the Braves.
Don Kelly went 4 for 4 with a home run and two doubles for the Tigers.
Shawn Hill started for the Tigers and allowed two earned runs in five innings. He was sent to Triple-A Toledo after his outing.
YANKEES: Derek Jeter is resigned to starting the season on the disabled list for the first time since 2001.
Jeter is undergoing treatment for his sore left ankle, still recovering from surgery last October. His last game action came as a designated hitter Saturday in a minor league exhibition.
“Of course, it’s disappointing,” Jeter said Tuesday. “I told you guys all along the goal was to be ready on Opening Day, and I didn’t reach it. I ran out of days. I pushed to try to get there opening day, and it didn’t work out. But I’ve still got to be ready for the majority of the season.”
Jeter could be activated for the April 6 game at Detroit.
CARDINALS: Placed third baseman David Freese on the 15-day disabled list with a lower back strain.
Infielder Ryan Jackson was recalled from Triple-A Memphis to replace Freese, who hopes to return in time for the home opener April 8
METS: Third baseman David Wright (strained intercostal muscle) played in his first minor league game since returning from the World Baseball Classic.
He went 1 for 5 and scored a run against Cardinals’ Triple-A and Double-A pitchers.