Freddy Galvis doubled to center field and Kevin Frandsen and Michael Young added singles to right. Galvis scored on Young's hit, but Frandsen got thrown out at third by Rays right fielder Matt Joyce.
Price then struck out Carlos Ruiz swinging before retiring John Mayberry on a force out to end the threat.
Frandsen hit a solo home run off Price in the third to push the Phillies' lead to 2-0, but that's all they got against the Rays left-hander.
Price allowed two runs on eight hits and struck out five in four innings. Of the 61 pitches he threw, 43 were strikes.
"I tried to make pitches, and that's a good team," Price said. "Whatever guys they have in the [World Baseball Classic] that didn't make the trip, they swung the bats very well. They had a good approach. You don't see that a whole lot in Spring Training, guys doing whatever they can to make the team. Guys who have the approaches I thought they did.
"I threw strikes, so that was good. I wasn't behind any counts. I was ahead. I kind of made it tough on myself letting hitters back into the count. I felt fine. It's part of Spring Training. One day you feel great, the next day you feel not so great. So I felt good today, I did. I'm not blaming what happened today on the way I felt or anything. They hit the ball, they hit the ball well. [Batting practice] was at 11 [a.m.], not 1:05 [p.m.]. So I didn't get the memo."
Kyle Kendrick started for the Phillies for his third outing of the spring. The 28-year-old right-hander is earmarked for the No. 4 spot in the Phillies' rotation after tying his career-high with 11 wins in 2012 while starting and pitching out of the bullpen.
After pitching two scoreless frames, Kendrick got touched in the third for an RBI double by Yunel Escobar and a two-run double by Evan Longoria that put the Rays up 3-2. That was the end of the scoring for the day.
Kendrick allowed three runs on five hits and a walk while striking out three in four innings.
The Rays' bullpen, including mainstays Kyle Farnsworth and Joel Peralta, allowed only two hits in five innings and struck out four.
Up next: Jeff Niemann will start when the Rays travel to Clearwater on Saturday afternoon to play the Phillies at 1:05 p.m. The game can be watched live on MLB.TV. Niemann, a 6-foot-9 right-hander, is in a competition with Roberto Hernandez for the No. 5 spot in the rotation. Also expected to see action are Jeremy Hellickson and Alex Colome. John Lannan is slated to start for the Phillies.