The power couple (along with J Lo's mom) hit up Yankees Stadium on Thursday night to watch NY take on the Boston Red Sox .... and you know they had to post the proof on social media.

Of course, A-Rod used to play for the Yankees ... but last night, he was bad luck -- the Yankees lost to the Sox 5-4, snapping the 8-game winning streak.

The good news ... Jenny's mom, Guadalupe, seemed to be having a blast at the game ... until the end.