Rodriguez fired two perfect innings against the Rays, striking out two in Boston's 19-2 victory. His importance will increase if Price is out for an extended period of time.
"It was encouraging, particularly in light of some of the early-morning news today," said Red Sox manager John Farrell. "In his first outing in Spring Training, he was in command. He was powerful in the first. I liked the way he used some secondary pitches in his second inning. He was able to get a quality two innings of work."
Before the injury to Price, Rodriguez was in a three-man battle with Steven Wright and Drew Pomeranz for the final two spots in the rotation. That could still be the case if Price makes a quick recovery.
For Rodriguez, the beauty of this Spring Training is being healthy from the start. He suffered a subluxation of his right knee early in camp last year and didn't fully recover until the second half of the season.
The left-hander turns 24 on April 7, and the Red Sox still feel he can develop into an upper-echelon pitcher. Rodriguez was 10-6 with a 3.85 ERA in his rookie season of 2015 before slipping to 3-7 with a 4.71 ERA last year.
Thursday was the first step toward a rebound.
"It was really good," said Rodriguez. "My mechanics, my shoulder, my knee, everything was normal. We'll see what happens. I threw pitches where I wanted. It was good."