This paper examines the effects of the Standard and Poor’s 500 (SP500) stock index crash during the global financial crisis and the COVID-19 pandemic periods on the South African top sector indices (basic materials, consumer goods, consumer services, financials, healthcare, industrials, technology, and telecommunication). The results of a copula-based BEKK-GARCH approach technique demonstrate the existence of price and volatility spillover during times of stock crashes. We discover that during a stock crisis, strong shocks and higher volatility spillover effects from the United States (U.S.) SP500 index to the top sector indices of the South African Johannesburg Stock Exchange (JSE) markets are more significant. However, there is no integrated economy, as the results did not show any spillover effects from South Africa to U.S. markets. Furthermore, the Gumbel copulas have higher dependence parameters, implying that extreme co-movements occur in the upper tails, suggesting the possibility of a large transmission of shocks from the SP500 to the eight top sector indices of the JSE and showing an asymmetric dependence between these markets. This result is important for investors willing to invest in the South African sector of equity markets to develop hedging strategies to prevent risk spillover from developed markets.