Maile singled and went to third on Cameron Seitzer's double before Shaffer hit a long fly ball to right field. Maile easily scored.
Rays starter Chris Archer threw four scoreless innings in his final spring appearance. Archer gave up three hits with no walks and six strikeouts. He threw 34 of 52 pitches for strikes.
"I actually felt really good about his changeup by the time he left the game," manager Joe Maddon said. "That was kind of neat. He was really, really good."
Archer hadn't pitched in a game since March 19, when he gave up three runs in 5 1/3 innings. He threw a simulated game Monday when rain in Florida canceled his scheduled start.
"It helped [Saturday] getting here and taking a walk around the ballpark," Archer said. "I strolled around, people-watched and gathered my thoughts."
The Biscuits rallied from a 5-0 deficit in the sixth inning against pitchers who are going to be Biscuits. Three Montgomery pitchers played for Tampa Bay on Saturday.
They scored four times in the sixth, highlighted by Jeff Malm's two-run home run off Dylan Floro. Taylor Motter hit the first pitch of the bottom of the seventh for a game-tying homer off Jimmy Patterson.
Catcher Justin O'Conner was a highlight for the Rays, though he's scheduled to begin the season at Class A Advanced Charlotte. O'Conner hit three doubles and threw out two potential basestealers.
O'Conner, who turns 22 on Monday, was a first-round Draft pick in 2010 and hit .233 with 14 homers at Class A Bowling Green last year.
"I was just excited to have a chance to be out there," he said. "I was pretty nervous at the beginning, but once the game started, it's still baseball. I was able to relax and have fun."
The Rays begin the regular season Monday at home against Toronto. The Biscuits open the year at home Thursday vs. the Birmingham Barons.
Stacy Long is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.