The two pitchers will start the season as the No. 2 starters on their staffs and each was making his final spring start.
Price looked especially sharp, holding the Twins to no runs on one hit while striking out six in four innings.
"We wanted to go out there and treat it just like a normal game," Price said. "We didn't want to work on stuff today. We were going to go out there and go after people, and that's exactly what we did."
Liriano also looked sharp during a five-inning stint. He limited the Rays to one earned run on seven hits while walking one and striking out seven.
Evan Longoria's two-out single off Liriano in the third drove home Jeff Salazar to give the Rays a 1-0 lead.
Luke Scott doubled off Liriano with two outs in the fifth, and Longoria followed with a fly ball to deep right that Lance Ray dropped, allowing Scott to score. Ben Zobrist followed with a double to put the Rays up 3-0.
Danny Valencia got the Twins on the board with a solo home run off Marquis Fleming in the sixth.
The Twins took a 6-4 lead into the bottom of the ninth, but Cody Rogers tied the game with a two-run blast off Matt Capps.
Up next: Jeremy Hellickson will start Tuesday when the Rays travel to Fort Myers to play the Twins at 1:05 p.m. ET on Gameday Audio. The right-hander will be making his final start of the spring prior to his first start of the regular season Sunday against the Yankees at Tropicana Field.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.