The BBC said the lights went out about an hour into the performance of the West End show, leaving critics to watch the stage comedy in near darkness.
"I haven't short-changed the meter," theater owner Cameron Mackintosh joked as he took the stage to explain what had happened.
The show continued after a short interruption with only emergency lighting to guide the players, the BBC said.
"It was fine. The audience went along with it, really," a theater representative said. "There was never any suggestion that it would be abandoned because it was the first night with all the critics."
"Power was interrupted to 16 customers in parts of Shaftesbury Avenue, Archer Street and Brewer Street in London following a fault on the underground electricity network at 8:13 p.m. yesterday," a spokeswoman for EDF Energy said. "EDF Energy Networks engineers worked as quickly and as safely as possible to repair the fault, with all customers back on supply by 10:43 p.m."