Pete Davidson and Emily Ratajkowski have gone as public as you possibly can in Hollywood -- attending an NBA game together ... sitting courtside, no less.

The new couple -- who've been maintaining a relatively low profile lately -- blew the doors wide open Sunday by crashing the New York Knicks' showdown with the Grizzlies, snagging the best seats in the house ... and not trying to hide the fact they were a pair whatsoever.

While there didn't seem to be any obvious PDA between them ... Em and Pete were all smiles, and not shying away from cameras either. In fact, the Knicks' own Twitter account posted a photo of them cheesin' it up, and tagging EmRat too.

It's pretty funny ... their presence was actually acknowledged during the broadcast, although the TV guys didn't seem to know who Emily was, 'cause they skipped over in the namedrop.

They also didn't seem to know PD all that well either ... completely butchering his name.

They were sitting next to Ben Stiller and Jordin Sparks -- so there was a lot of star power in the house. But for Pete and Emily to pop is a big deal, seeing how they've seemingly been trying to lay low as they've hit the town in and around NYC.

They were spotted hanging 2 weeks ago in Brooklyn -- the first time they'd been seen on camera amid rumors they were linking up. Pete did something similar with Kim Kardashian ... trying to keep it on the DL for a while, then finally embracing the spotlight.

Seems like he's fast-tracking things this time around, though ... nothing says we're dating like a night out at MSG during primetime TV.

Say hello to the hottest new item in the Big Apple!