The Rays held the lead for much of the day thanks to catcher Rene Rivera, who lined a solo shot out to dead center field, just over the 405-foot sign, with one out in the first inning.
The Twins didn't counter until the sixth, when Kennys Vargas unloaded for a two-out solo shot off reliever Jeff Beliveau. The blast, his fourth of the spring, carried over the left-field berm and nearly out of the stadium.
This was a big start for Andriese, who is competing for a spot in the Rays' rotation. He retired his first six hitters before giving up a double to Eduardo Nunez, went 2-for-3 to raise his average to .412. But Andriese stranded two runners in the inning, then one apiece in the fourth and fifth.
The 25-year-old, looking to make his Major League debut, completed five innings in his longest outing of the spring. He gave up three hits and one walk while striking out six.
"I thought I commanded the strike zone with the sinker today," Andriese said. "Just throwing all of my pitches for strikes. The cutter was good on both sides of the plate and the sinker as well."
Gibson also enjoyed his strongest outing. Rivera's homer was one of only two hits he surrendered over six innings, to go along with two walks and seven strikeouts. In 41 career regular-season outings, the righty has struck out seven or more only three times.
"I'll take the next two outings and keep trying to get sharp and just keep the consistency," Gibson said. "You're never exactly where you want to be at this game, so still working on things and still trying to iron things out."
The Rays put runners at the corners with two outs in the seventh, on singles by Desmond Jennings and Tim Beckham, but Casey Fien induced a groundout from John Jaso to preserve the tie. In the bottom of the eighth, Aaron Hicks led off with a single, then stole second on Brian Dozier's strikeout, but the Twins couldn't cash him in against C.J. Riefenhauser.
Up next: The Rays will have a "bullpen day" on Thursday afternoon with Kevin Jepsen getting the start against the Yankees in the 1:05 p.m. ET contest which you can watch live on MLB.TV. Jepsen will pitch at the back-end of the Rays' bullpen during the regular season. Also expected to see action are fellow relievers Ernesto Frieri, Brad Boxberger, Jordan Norberto, and Kirby Yates.