The Rays ace allowed a home run to Jason Kubel on a 1-0 pitch in the second.
"It felt good to finally hit one hard," Kubel said. "The results aren't there, but I feel like over the last few games, my last four or five at-bats are feeling pretty good. So if it keeps getting better each day before the season starts, I'll be right where I want to be."
Price otherwise looked sharp during a five-inning stint in which he allowed one run on three hits and a walk while striking out eight.
"It got better as the game went on, absolutely," Price said. "The first two innings, I kind of felt like I did 10 days ago -- couldn't slow myself down on the mound. Made some adjustments with [pitching coach Jim Hickey] and [Jose] Molina, and after that second inning, I felt pretty good."
Eight strikeouts? Kind of surprised by that? What was working?
"My cutter and my slider were really good -- throwing it to the back-door side to a righty and then throwing it in to a righty as well. It's something I've been working on that was really good today. And my curveball, it's definitely the best it's been in six months."
Ricky Nolasco started for the Twins and allowed an RBI double to Yunel Escobar in the second. David DeJesus singled him home to give the Rays a 2-1 lead.
Nolasco, who will likely be the Twins' Opening Day starter, allowed two runs on four hits while striking out one in four innings.
The Rays scored at least once in each of their last four innings.
Scott Diamond took over for Nolasco to start the fifth, and he got into a bases-loaded jam that saw Molina score on a sacrifice fly, but escaped further damage by retiring Evan Longoria on a ball back to the mound for the third out. The Rays tacked on one more against Diamond on Matt Joyce's groundout in the sixth.
In the seventh, Jeremy Moore knocked a two-run homer -- his second of spring -- off Twins reliever Ryan Pressly, and in the eighth, Curt Casali's double off Caleb Thielbar drove in Brandon Guyer.
Up next: Right-hander Kevin Correia is set to make his second Grapefruit League appearance on Wednesday against the Pirates in a 12:05 p.m. CT start at Hammond Stadium. Correia has been sharp so far in spring, and he has also made appearances in an intrasquad game and a "B" contest. Right-hander Gerrit Cole is slated to start for Pittsburgh. Watch the game live on MLB.TV.