Pete Davidson & Kate Beckinsale Make Out at Hockey Game

Pete Davidson and Kate Beckinsale are going strong one month after they were seen together hand-in-hand -- and now ... they're pouring their romance on the rocks.

That bad ice joke is just a fun way to say that Pete and Kate are taking in some hockey Sunday in NYC, where they're watching a close game between the New York Rangers and the Washington Capitals (it's 2-2 in overtime as of this writing).

Check out their view -- primo seating right behind the team's bench ... even though it looks like they couldn't keep their eyes off each other.

This day date is actually a follow-up to another outing for the rumored couple just the night before. Pete and Kate were spotted leaving an 'SNL' after-party Saturday night after Pete got done taping the show. They were holding hands again ... so yeah, they seem to be a thing.

Remember, Pete and Kate left one of Pete's shows back in February in similar fashion ... handsy all the way through with Pete leading the way.

His ex-fiancee, Ariana Grande, gave her blessing not too long afterward, saying they looked great together. It's true ... they really do.