Cosart singled off All-Star Jacob deGrom to lead off the third inning. It was the Miami starter's first plate appearance of camp, and he made the most of it by slapping the ball down the first-base line.
The more surprising hit came in the ninth by Rienzo, who is 0-for-2 in his career. He drew a tough assignment, facing Jeurys Familia, one of the top closers in the NL.
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Rienzo's double seemed improbable, especially after he awkwardly swung and missed at a previous pitch. It brought plenty of smiles from the Marlins' dugout.
In the first half of Grapefruit League games, the Marlins used the designated hitter. Pitchers started to hit on Saturday.
"If a guy can help himself, he's going to be better," manager Don Mattingly said.
Although they didn't hit in games, pitchers have been hitting on the back fields of the Roger Dean Stadium complex.
"We've been hitting for a while," Mattingly said. "They've actually been hitting all over the place. It's really why we start hitting at this time, because guys are going to have to do it during the season."
• Cosart bolsters case for rotation spot
Cosart is a versatile athlete, but he broke into the big leagues with the Astros, so he didn't get many plate appearances in the American League. He's 5-for-38 (.132) in his career.
One of Cosart's big league hits came in 2014, and it was also off deGrom. It happened to be a big hit since it snapped deGrom's streak of striking out the first eight batters he faced.
deGrom would have set a modern-day record if he had fanned Cosart, who singled to right on Sept. 15. The only other pitcher to strike out the first eight batters he faced was Jim Deshaies in 1986.
"I got one in the game he struck out eight in a row," Cosart said. "It was the same pitch, fastball away. That's about the only chance I have. He threw me a slider at 1-1 [Monday]. I was like, 'Alright, I'm going to get a fastball, might as well close my eyes and swing.'"