The protesters used mobile phones and strong flashlights onto the emblematic Unesco World Heritage building on Tuesday night to disrupt a six-minute light show promoting the country's richest horse race.
They chanted "sails are not for sale", referring to the shape of the building which is similar to the sails of a ship, the Australian media reported.
The controversial advertising for the race, which boasts 13 million Australian dollars ($9.25 million) in prize money, has seen groups ranging from politicians to media personalities debating whether a sport centring on gambling should be promoted on the heritage-listed venue.
Up to 3,000 people crowded the city's area, while an online petition to the New South Wales (NSW) state government against using the structure as a "promotional billboard" garnered more than 200,000 signatures, reported the Nine News channel.
State Premier Gladys Berejiklian did not rule out using the venue to promote other events and told the media that she did not want the state to "fall behind" in tourism.
"I encourage the input and say people protest for governments to listen -- and we do that -- but I also say people on all sides of the argument should be respectful," Berejiklian told national broadcaster ABC.
The original plan of Racing NSW, the horse-racing agency of New South Wales, was to hold a live barrier draw and project the results onto the facade of the famous Opera House, as well as illuminate the building with the jockeys' colours alongside The Everest logo, but the agency had to cancel the plan due to security reasons.
One of the protesters, Joshua Richardson, 19, told ABC that "it's completely wrong to have one of our national landmarks used as a billboard. It's nationally embarrassing".
Berejiklian gave the green light to the promotion despite the opposition from Louise Herron, Executive Director of the Sydney Opera House and the online petition opposing the decision.
The New South Wales Heritage Board also expressed its "extreme disappointment" over Berejiklian's decision, which was backed by Australian Prime Minister Scott Morrison.
(With inputs from agencies.)