Lady Gaga In The Mood ... For A Surprise Show

7/27/2016 10:00 AM PDT
EXCLUSIVE

Lady Gaga crashed the stage at a ritzy jazz club for a surprise worth WAY more than the price of an Old Fashioned.

Gaga flew under the radar in the audience at Rose Bar's jazz night Tuesday in NYC ... that is, until she grabbed the mic. We're told it even surprised the staff, who closed the doors after she took the floor.

Check out the video ... the entire room is hanging on her every note.

Witnesses tell us Gaga sang for about 30 minutes and even played the drums in front of the intimate 50-person crowd. Afterward, she mingled and sipped cocktails until close.