Alex Rodriguez was just trying to talk some baseball during American League Championship Series coverage on Monday ... when Boston fans used it as an opportunity to ruthlessly troll the hell out of him about Jennifer Lopez and Ben Affleck.

A-Rod -- who's doing analysis for Fox's coverage of the postseason -- was hit with verbal jabs before and after the Red Sox beat the Astros ... with fans in the crowd chanting 'J Lo' and 'Aff-leck' and even more harsh phrases like, "She left you with Ben Affleck!"

Of course, J-Rod split back in April ... with Lopez moving on with her former fiancé. Boston fans -- who absolutely hate the ex-Yankees slugger -- made sure A-Rod didn't forget their Sox superfan is living it up with J Lo now.

There were more NSFW chants, which kept the worker controlling the censor button busy all night ... but no matter what was thrown his way, it appeared A-Rod was unfazed.

Another guy yelled out, "Hey, A-Rod, what's your favorite Ben Affleck movie?!"