Lady Gaga Brings Out Bradley Cooper During Vegas Show to Sing 'Shallow'

Lady Gaga had a surprise guest Saturday night in Vegas ... her co-star and director of "A Star is Born" -- Bradley Cooper, and he did not disappoint.

Gaga was performing her 'ENIGMA' show at the Park Theater at Park MGM when Bradley appeared on stage, and people in the crowd went wild.

They sang a duet of their song "Shallow," after B.C. overcame some difficulty in installing his earpiece.

It's a super smart move ... Bradley and Gaga are best up for Oscars -- Best Actor and Best Actress -- and this type of publicity keeps them and the film front and center.