Alex Rodriguez: Tagging Fastballs, Kate Hudson

Alex Rodriguez went 1-for-3 with a run in the Yankees' 4-3 win over the Rays yesterday ... then may have scored in a different way later that night!

Enjoying a swanky evening out, the Rod and rumored fling Kate Hudson were spotted out and about in New York City at the famed 40/40 nightclub.

They exited separately to avoid being photographed together, but don't think it was a coincidence that both happened to be there at the same time ...

K-ROD: Kate Hudson and A-Rod step out again in N.Y. City.

Kate Hudson looked sexy in a teal green dress with black heels, while Alex Rodriguez was his casual, handsome self in a button-up shirt and jeans.

Rumors that A-Rod and Kate are dating popped up two weeks ago, then were fueled by Hudson's frequent visits to Yankee Stadium to see her man.