Rumer Willis (left) and Demi Moore
Gilbert Flores/Celebrity Photo
11/06/2013 at 01:00 PM EST
Nobody nurses a broken heart better than mom.
While a source tells PEOPLE Rumer Willis and boyfriend Jayson Blair, 29, have split after more than a year together
, the actress, 25, put on a brave face and hit the stage at Sayers Club in Hollywood Tuesday night for her weekly performance.
Looking "refreshed and vibrant" in the audience was mom Demi Moore
, 50, who sipped on a can of Red Bull and clapped and whistled enthusiastically after each song her daughter performed, says an onlooker.
"Rumer seemed really happy that her mother had come out to support her," adds the source. "Right after she got off stage, the two had a really sweet mother-daughter moment."
Clad in a black dress, boots and a long gray sweater coat, Willis sipped on a cocktail before her performance, which included covers of Amy Winehouse
's "Valerie" and Miley Cyrus
's "Wrecking Ball."
Later in the evening, the budding singer and her mom danced to Icona Pop's "I Love It" before heading out with some friends just after midnight through a side entrance.
With reporting by Jennifer Garcia