A$AP Rocky Sweeps Rihanna Off Her Feet During Late-Night NYC Date

A$AP Rocky and Rihanna are riding off into the sunset -- or the sunrise, rather ... and we mean it in every sense of the word, 'cause a late-night date night turned into just that.

The A-list couple kept their love fest going Saturday night into the wee hours of Sunday morning ... where we're told they popped up in the lower east side of NYC after a night out, walking hand-in-hand -- and, before long, body-in-arms thanks to A$AP swooping her up.

Check out the video we got of that exact moment ... it's like straight out of a movie, and RiRi seemed to be digging every minute of it. Eventually, they drove away in a waiting SUV.

BTW, we're told this was shot around 5:30/6 AM Sunday -- so yeah, it was definitely a marathon date they were on. Eyewitnesses also say they came across a dude who seemed drunk and sprawled out over the floor ... to which A$AP/RiRi said ... yo, help him out!

Unfortunately for him, his buddies seemed to be starstruck with this sighting ... and for good reason. It's not every day you might spot this -- but then again, maybe that's changing.

Frankly, A$AP and Rihanna have been spotted out and about all over town lately ... and are NOT shy to show off their PDA, this weekend included, it seems. They're clearly gaga for one another -- and apparently want the whole wide world to know it.