John Lackey took the loss for Boston, giving up five runs and six hits in 5 1/3 innings. He walked three and struck out four while throwing 96 pitches, 57 strikes.
Price went 6 1/3 innings, allowing one run and five hits with two walks and seven strikeouts. He threw 103 pitches, 61 for strikes.
The 2010 AL Cy Young Award runner-up will get one more Grapefruit League start, expected to be a short tuneup before the April 1 season opener against Baltimore.
"I'd like to get my slider back to where it was," Price said. "It wasn't very good today. But my curveball was pretty good."
Lackey gave up two home runs but was pleased with his outing.
"Felt good physically," he said. "I was really happy with how my arm felt, for sure. Stuff-wise I feel like I'm ready to go."
Red Sox manager Terry Francona was satisfied with Lackey's performance, too.
"For the most part pretty good," Francona said. "I thought he made a couple mistakes. I thought the first home run I didn't think was a home run. I thought the second one was. But I thought he followed the glove pretty well. I thought he threw some good off-speed pitches. He got up to [96 mph] and that's good, that's important. Next time he'll scale back. But I thought his stuff was pretty crisp."
Lackey said he feels further along this spring than he has in several seasons.
"I was definitely being a little careful last spring training," he said. "But I pushed it a little bit as far as more long toss and more effort level I guess during my starts, throwing the fastball, I guess."
The Rays opened the scoring in the second on Johnson's drive to right field.
"I'm starting to kind of feel it out there, where you'd like to be at the start of the season," Johnson said.
Ramirez went 1-for-1 with two walks and scored a run.
Jose Lobaton, who was 2-for-2 with two runs scored, led off the third with his first home run of the spring, giving the Rays a 3-0 lead. Matt Joyce went 2-for-5 with a run and Reid Brignac was 2-for-4 with a run and an RBI.
Red Sox minor leaguer Aaron Bates hit his first home run of the spring, a three-run shot in the eighth inning off Cory Wade. Dustin Pedroia and Jason Varitek each went 2-for-3 for the Red Sox, who have their only off day of the spring Wednesday.