HONG KONG’S political battleground has expanded. Protesters who in June demanded cancellation of an extradition bill that would make it easier for suspects to be transferred to mainland China are now asking for greater democracy and an investigation of police brutality. The demonstrators have shifted tactics, too, from sprawling marches to smaller, unpredictable flash-mobs, as well as intrusions such as the airport protest on Monday that led to massive flight cancellations. China’s leadership has misread the situation from the start. Time to get this right.

China gained control over Hong Kong from Britain in 1997, pledging autonomy for a city that has come to define capitalism and freedom in Asia. Gradually, China has been whittling down those liberties, including by suppressing the “Umbrella Movement” in 2014, refusing to allow direct elections for chief executive, kidnapping five Hong Kong booksellers and attempting to impose the extradition bill. When protests erupted over the extradition proposal, Hong Kong leader Carrie Lam should have immediately canceled it. Instead, Ms. Lam, more sensitive to the demands of her overlords in Beijing than to the values that underlie Hong Kong’s success, tried to sidestep the issue with some obfuscation. It didn’t work.

Another miscalculation was to assume that the protests would simply flare out. The protests are a political groundswell, a reflection of genuine popular anger and commitment to democracy. But authorities treated the protesters as “terrorists” and “rioters,” a law enforcement problem to be handled by the Hong Kong police, who have repeatedly overreacted, including this weekend when they fired tear gas into a subway station and were discovered using undercover officers to infiltrate the demonstrators. In response, some protesters have turned more violent, unwisely resorting to vandalism, throwing bricks and a petrol bomb, and disruption.

Yet another mistake of the Chinese authorities has been to roll out the boogeyman that the protests are inspired by foreigners. China’s state media have trotted out the ghost that seems to frighten all authoritarians, calling the protests a “color revolution” instigated by the United States. The charge seems almost comical given President Trump’s lack of sympathy for democracy movements anywhere in the world. But it speaks volumes about paranoia in the Communist Party that holds a monopoly on power in China. This protest movement is very much indigenous to Hong Kong and its people.

Lately, there have been dark hints of a stronger crackdown by the military. But repeating the catastrophe of Tiananmen Square would be terribly counterproductive; hopefully China’s leaders understand as much. They might be hoping to slowly strangle the protest movement without violence and without giving an inch. This would be yet another miscalculation because the pent-up demands of this summer won’t go away.

The right answer for President Xi Jinping and for Ms. Lam, if she remains in office, is to open serious negotiations with the protesters on their demands, which are quite reasonable. Cinching the noose ever tighter, as the Chinese government has done in recent weeks, is the pathway to a dead end that could harm both Hong Kong and mainland China economically as well as politically. A cliff looms, and China’s leaders should turn back before it is too late.