A funeral was held Monday in the Osmonds' native Utah for the 18-year-old, who had long suffered from depression and apparently leaped to his death last month from the eighth floor of his apartment building in Los Angeles.
Donny and Marie Osmond canceled their subsequent dates at the Flamingo Las Vegas, but resumed performing Tuesday night.
"The way Osmonds survive is we keep singing," People.com reported Marie told the audience on her first night back to work. "That's what we want to do tonight. I know my son would want that and this show is for him."
"I think we need to give a big round of applause for my sister for even coming on stage," Donny told the crowd, which then gave Marie a standing ovation.