The Marlins had just one hit entering the eighth, but they responded with seven hits in the game-changing frame.
"It was nice to put some runs on the board and have a nice comeback," manager Mike Redmond said. "It's always nice to win in Spring Training."
While Owens struggled, fellow left-handed prospect Brian Johnson allowed one run on one hit over 3 2/3 innings. He struck out five and walked three in his 67-pitch performance.
"Physically, I felt great," said Johnson. "A little excited at times; obviously it showed. Four-pitch walks, which is not what I like to do, so I got upset with myself, especially because I had such good defenders behind me. That's what bothers me the most, but I talked to [manager] John [Farrell] and [coach] Bob Kipper, who's here today, and I figured out what it was, and that's why that last inning I felt more like me."
Boston had broken the game open with a four-run third inning off Tom Koehler, who settled and worked six innings for Miami. The Red Sox sent eight to the plate, collecting four hits, including doubles by Allen Craig and catching prospect Blake Swihart.
Koehler, Miami's expected No. 5 starter, struck out five and walked two while running his pitch count up to 80.
After retiring six of the first seven he faced, Koehler ran into trouble in the third, allowing four runs on four hits. Jackie Bradley Jr. got the inning going with an infield single. Koehler made a throwing error on a pickoff, allowing Bradley to reach second and then score easily on Swihart's liner to deep left.
The inning got away from Koehler after he walked Jemile Weeks. Hanley Ramirez floated a soft fly ball that dropped near the line in short right field, loading the bases. Craig crushed a ball to right-center that was held up by the wind; otherwise it had a chance to be a grand slam. The double cleared the bases.
"It feels good to hit the ball to right-center," said Craig. "I've typically been pretty good at hitting the ball there in my career and I put a good swing on it."
The lone hit Johnson yielded resulted in a run. In the third inning, Reed Johnson swatted an RBI single to right, scoring Hechavarria from second.
Up next: The Red Sox have the only off-day of their game schedule on Wednesday, though right-hander Justin Masterson will pitch in a Minor League game. The club returns to action for a 1:05 p.m. ET game against the Twins on Thursday at JetBlue Park. Lefty Wade Miley gets the start. Edward Mujica, Craig Breslow and Alexi Ogando are scheduled to get work out of the bullpen.