Garza, the Twins' Minor League Pitcher of the Year last season, and Schilling, penciled in as the Red Sox's opening day starter, each pitched two scoreless innings in a 4-4 tie in 10 innings Wednesday night.
"It was a blast," Garza said of pitching against Schilling in both teams' exhibition opener. "There's no pressure on me. I got up (to the majors) in a year. That's more than I can ask for."
Garza, 23, won his first five decisions at Triple-A Fort Myers last season and was a combined 14-4 before making his major league debut on Aug. 11. On Wednesday, he struck out David Ortiz on a slider in the first inning.
"We just want him to do what he did tonight," Twins manager Ron Gardenhire said. "Throw the ball down, attack the hitters and make them swing the bat."
Schilling allowed two hits and the Red Sox led 4-1 before Julian Tavarez allowed a three-run homer in the fifth by Joe Mauer.
"I felt a little stronger than I thought I might be," said Schilling, who threw 19 pitches -- 18 fastballs and one slider. "I feel like I'm good to go for a lot more than that right now."
Francona said he didn't think it was worth it to change his plan and send out Schilling, who threw 15 strikes, for a third inning even though he hadn't thrown many pitches.
"He got two innings under his belt and he threw strikes," Francona said.
"I was nervous and short of breath and all the things I normally am whether I'm facing Northwestern or the Yankees," Schilling said. "It's that first time out, that anxiety."
The Twins had taken a 1-0 lead in the third against Boston closer candidate Joel Pineiro on a single by Jason Bartlett, a throwing error by shortstop Julio Lugo and an RBI single by Rondell White.
Boston went ahead 4-1 against Scott Baker with two runs in both the third and fourth innings. Lugo and Ortiz singled in runs in the third and Jacoby Ellsbury doubled home two in the fourth.
The Twins nearly took the lead in the ninth, but right fielder Alex Ochoa turned a double play by catching Alexi Casilla's fly ball and throwing out Luis Rodriguez at home after he tagged up.
"As soon as it was hit, I said, 'Oh, no, he can throw,'" Gardenhire said.
Francona said, "That's one of the better baseball throws you'll ever see."
Ochoa, a long shot to make the Red Sox, also threw out a runner at second in the fifth.
Before the game, a statue was unveiled of former Red Sox star Ted Williams in front of City of Palms Park. His former teammate, a tearful Johnny Pesky, 87 participated in the ceremony. ... Twins first baseman Ken Harvey will miss at least 3-4 days after pulling a chest muscle on his first swing. Center fielder Torii Hunter is day to day after bending a fingernail back while sliding.