Alex Rodriguez proved he's a baller on the baseball diamond and the hardwood ... 'cause he tossed up a shot Sunday from halfcourt and made it -- helping out one lucky student in the process.

The former Yankees third baseman was in attendance to watch Army take on Bucknell University Saturday afternoon in basketball ... and, during halftime he was invited to take a huge shot from the middle of the floor.

Check out the vid ... A-Rod -- clad in a bright orange Bucknell t-shirt -- tosses the ball up, hits the backboard and the ball goes straight through the hoop.

It's a Steph Curry-level make, and the crowd goes absolutely berserk -- especially one kid who's gotta be an A-Rod fan for life ... 'cause he made $10K after A-Rod sank the basket.

Rodriguez scoops the student up into a big hug right after he won him the money ... a moment that has to feel more like a dream than real life for this lucky fan.

BTW ... Bucknell crushed Army, 84-53 -- so, it was a pretty darn good day all around for Bucknell U.

Alex hit 696 homers during his big league career ... and, he's now got one cash-winning halfcourt shot under his belt too!