The southpaw tossed against the Yankees extended spring squad, who were joined by Alex Rodriguez -- in the final days of his rehab back from a strained right quadriceps.
Price twice got the three-time American League MVP to strike out, allowing Rodriguez one hit -- a solo homer over the right-center fence at the Al Naimoli Complex in St. Petersburg, the Rays' Minor League facility.
"He's a competitive guy, I'm a competitive guy and everybody has pride," Price said. "So it doesn't matter who are you are facing, you want to get them out and want to throw good pitches."
The young hurler said the fastball Rodriguez hit over the fence was something he would "make a mental note" of and learn from.
"He's arguably one of the best players in baseball," Price added.
Rodriguez had similar praise for the Price, who tossed a blistering fastball with speeds around 95-97 mph for the majority of his five innings. The young hurler previously topped out at 100 mph, in a Spring Training game against the Yankees.
"I wish he was on our team," Rodriguez said. "He has a very bright future. The Rays are doing a fantastic job of drafting these young guys."
The No. 1 overall pick in the 2007 First-Year Player Draft, Price had an impressive spring. After being hampered by tightness in his left shoulder, the hurler appeared in two spring games, garnering a 0.00 ERA and retiring six of the seven hitters he faced.
Following Spring Training, Price experienced a minor strain in his left elbow, and the Rays cautiously placed him on rehab assignment in St. Petersburg.
With five successful innings on Saturday afternoon -- including 10 strikeouts -- Price is now slated to join Class A Vero Beach and make his professional debut on Thursday in Vero Beach against Clearwater.
"It's been tough," Price said of the eight weeks he's been on assignment. The hurler credits the Rays' training staff for getting him back to where he was coming into Spring Training, and says his teammates and coaches have made the difficult rehab process more bearable.
Thursday's start will mark Price's first game in more than a year, and the Vanderbilt alumni was clearly excited at the prospect.
"It's been a while since I've thrown that many pitches, and it definitely took a toll on me there at the end," Price said. "I worked hard, but I'm back at it now. ... It's time to get into a real season."
Brittany Ghiroli is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.