He allowed a game-opening single to former Pirates outfielder Alex Presley, who was caught by Martin attempting to steal second. Rodriguez surrendered another single to Trevor Plouffe with one away in the second, then retired the next two men.
"I was very pleased with his performance," manager Clint Hurdle said. "He had a very comfortable approach, and worked in his curveball in the second inning. We're real happy with the steps he's taken forward this spring."
Rodriguez confirmed using his curve more this time than in his previous outing, a scoreless inning on Monday against Tampa Bay.
"I was missing my spot early with the curve, so I kept throwing it until I could get it over for a strike," Rodriguez said. "So I threw everything, and didn't feel anything [bad]."
After going through a slower program than other pitchers in the early stages of Spring Training camp, Rodriguez is now on a regular fifth-day schedule. He is due to stretch out to three innings in his next start, which should come on Wednesday, again against Minnesota, in Fort Myers, Fla.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.