The former superstar tight end came to the realization during his appearance on the "Up & Adams Show" ... when he was checking out footage of Austin Capobianco and fellow NYY fan, John Peter, interfering with Betts after he snagged the ball out of the air.

Gronk had an aha moment in real time ... seemingly completely unaware of his connection to one of the fans prior to joining the show.

"That guy right there grabbing Mookie Betts' glove was my friend in college," Gronk said.

Gronk is a proud Arizona Wildcat ... and played college football in Tucson from 2007 to 2009 ... the same time Capobianco also roamed the campus.

"He was on the hockey team, the club Arizona Wildcats team ... and let me tell you, the whole hockey team -- they were absolute maniacs," Gronk said.

"Him doing that represents him very well."

The four-time Super Bowl champ also praised Capobianco for making the most of his viral moment ... saying Austin has always been about his teams and will do anything to see them succeed.

"He is all in for his teams," Gronk said, "He is all in for the Yankees."

Now, Gronk isn't defending Austin -- he feels the move was bad for sports -- but understands that fans, like Capobianco, will go to extremes.

Unfortunately for Capobianco and Peter, they were booted from the venue ... missing out on the home team's first win of the World Series.