Cora posted the photo to his Instagram account on Sunday night, while the Patriots dispatched the Green Bay Packers 31-17.
The Red Sox skipper even referenced Brady's nickname as the G.O.A.T. (greatest of all time).
"Me with the [goat emoji]," Cora wrote for the Instagram caption on the photo of himself with the five-time Super Bowl champion.
Cora, 43, is just two years younger than Brady. The longtime infielder for the Los Angeles Dodgers, Cleveland Indians, Red Sox, New York Mets, Texas Rangers and Washington Nationals made his Major League Baseball debut in 1998.
Brady entered the NFL in 2000. The Red Sox hired Cora in October 2017. He led the team to a franchise record 108 wins and a championship in his first season.
Cora and the Red Sox took the field -- along with the World Series trophy -- while riding a duck boat into Gillette Stadium in Foxborough, Mass. Brock Holt, Steve Pearce, J.D. Martinez, Ryan Brasier, owner John Henry and president and CEO Sam Kennedy were also in attendance.
"I got the privilege to see the faithful during the duck boat tour, and it was awesome," Pearce said, according to Patriots.com. "There was just fan after fan after fan. To bring the championship home to Boston, to see the love you hear about from everybody too, the Patriots or the Celtics, I'm glad we're keeping the tradition going."