The Red Sox center fielder stepped up to the plate as the sixth batter in the bottom of the third inning as Boston trailed 4-2. He worked a 2-1 count against Astros starter Gerrit Cole before smacking a 97.8-mph fastball to left field, scoring Xander Bogaerts, Steve Pearce and Rafael Devers.
The double gave Boston a lead it would never surrender as the Red Sox bullpen allowed just one run over the final six innings.
"They did an outstanding job and they've done it throughout the postseason," Red Sox manager Alex Cora told reporters. "We trust those guys. There's certain matchups we like with them and we're going to try to go to those matchups."
Boston took its initial lead in the bout with an Andrew Benintendi RBI single in the bottom of the first inning. Rafael Devers also had an RBI single in the same frame, putting Boston on top 2-0 early on.
Astros star George Springer tied the score at 2-2 in the top of the next inning, hitting a two-run double off of Red Sox starter David Price. Marwin Gonzalez gave Houston a 4-2 edge with a two-run homer in the top of the third inning.
Bradley arrived at the plate in the bottom of the frame to snatch away the Astros' momentum.
Boston pushed its lead to 6-4 on a passed ball in the bottom of the seventh inning, before Mookie Betters plated Devers on an RBI double in the eighth inning.
Jose Altuve plated the Astros' final run with an RBI single in the top of the ninth inning.
The series returns to Houston for Game 3, with first pitch coming at 5:09 p.m. on Tuesday at Minute Maid Park.