HONG KONG—Pro-democracy protesters and police clashed in Hong Kong’s financial district Sunday, as authorities abruptly shut down an approved and largely peaceful rally and used batons and tear gas to disperse the crowd.

Thousands of people—many wearing the black garb and masks now synonymous with a protest movement that is in its eighth month—gathered in the city’s Central district in the midafternoon to demand universal suffrage. Some were waving British and American flags and calling for international support for their...