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.
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 Phillies' bullpen -- Michael Stutes, Mike Adams and Aaron Cook -- allowed only two hits in four innings and struck out three.
Up next: The Phillies return to Clearwater to play the Rays at 1:05 p.m. on Saturday at Bright House Field. The game can be watched live on MLB.TV. Left-hander John Lannan, who will be the Phillies' fifth starter this season, is scheduled to start. Phillies closer Jonathan Papelbon will make an appearance. He has been roughed up in two appearances, and missed another appearance this week because of illness.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.