Bradley's lengthy leap helped the Red Sox hold on for a 2-1 win on Wednesday at Oriole Park at Camden Yards in Baltimore.
"Big-time circumstances," Bradley told reporters, according to MLB.com. "If you don't catch it we go home."
Mookie Betts hit a solo homer in the third inning of the victory. Boston held the 1-0 lead through five innings, before Trey Mancini doubled in Joey Rickard for the tying run in the sixth frame. Neither team could plate a run for the next three innings, sending the game into extra innings.
Boston and Baltimore continued to put eggs on the scoreboard in the 10th frame. Chris Davis led off the bottom of the 11th inning with a strikeout, before Mancini returned to the plate. The Orioles utility man went down 0-2 in the count before slamming a fastball to deep center field.
Bradley sprinted to the warning track and elevated high above the outfield wall, before reaching his arm over the fence and snagging Mancini's effort, stealing the game from Baltimore.
"It's one of the worst feelings you can describe," Mancini told reporters. "I didn't get my hopes up too much. I've hit too many balls to center that I thought were hits and Jackie has come down with."
"I didn't want to get too excited until it went over the fence."
Renato Nunez struck out in the next at-bat to end the inning. Bradley began the next frame with a groundout. Sandy Leon followed with a strikeout for Boston. Then Andrew Benintendi stepped into the box. The Red Sox left fielder -- who had a front row seat for Bradley's grab -- smacked a 2-1 fastball over the right center field fence for a go-ahead solo homer.
Red Sox reliever Heath Hembree struck out the Orioles in order in the bottom of the inning to seal the victory.
Bradley was 0-for-4 with a walk and two strikeouts at the plate in the loss. Benintendi was 1-for-6 with a run scored, an RBI and a strikeout for Boston.