We're told Miley arrived first (she's a regular at the place) ... with Justin showing up around 1:50 AM and heading straight for Miley's table.
We're told the two hung out for roughly 15 minutes ... laughing and flirting together ... and they both left the theater at the same time, just after 2 AM. It's unclear where they went after the show.
Hours before the late-night rendezvous, Bieber's leopard-spotted Audi was seen leaving Miley's L.A. home on Saturday.
FYI -- Miley and Bieber have been friends for years ... but it seems like there might be something more going on between the two.
Miley just responded, saying there's NO WAY she's hooking up with Bieber ... she's engaged.