When Jackman realised he was getting beaten, the 45-year-old X-Men star made a terrible but hilarious attempt to cheat, placing one of Fallon's out-of-play balls back on the table when the host's back was turned.
"I tried to cheat, but I put my own ball back out there," Jackman confessed.
"It's a really bad moment for me."
Afterwards, Jackman recounted his experience performing at Joan Rivers' funeral on Sunday, and revealed that the US comedian had approached him about singing at the memorial service years ago after seeing him star in Broadway musical The Boy from Oz.
"When Joan Rivers asks, you just answer," Jackman told Fallon.
"She had planned everything out. She had seen me in a show called The Boy from Oz ... and I sang a song from that. It was called, Quiet Please, There's A Lady On Stage.
It's a beautiful celebration of a woman, and it was for her, and the entire audience in the synagogue got up and started clapping and cheering.
"The whole thing was very uplifting, very touching and moving, but funny."
Rivers, 81, died a week after suffering a cardiac arrest during a routine throat operation.
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- AAP