It all went down at Spring St. Bar in Downtown L.A. -- Eric rolled in with some buds and his girlfriend (Tatyana Ali) around 11pm ... just hours after taping an interview with the Ginger One.
According to sources on scene, one of Eric's friends waited 'til the time was right -- then proudly announced to the bar that Eric was about to appear on "Conan" ... and asked everyone to watch.
Bar management thought it was cool ... so they shut off the music and turned up all the TVs.
Thankfully, the segment was pretty funny -- we're told the bar crowd didn't mind the brief interruption ... and even laughed a lot.
Check out the "Conan" segment below.