This paper examines the volatility spillovers and the time-frequency dependence between crude oil and stock sectors in the U.S. and China using both wavelet coherence and asymmetric BEKK GARCH models. This study also investigates the impact of the COVID-19 pandemic on spillover effects and portfolio management. The results reveal strong positive co-movements between WTI oil and US sector stock returns at medium and low frequencies particularly in 2020Q1. We find significant long-term co-movements between oil and Chinese sector stock returns (64–128 days). Furthermore, the findings reveal a significant and asymmetric volatility transmission between oil and sector stocks in both the US and Chinese economies. The evidence of spillovers is more pronounced during the COVID-19 period. It is recommended that equity investors should hold more stocks than oil assets to minimize risk without reducing the expected return. Finally, hedging with oil is expensive for U.S. sectors during the pandemic but inexpensive for Chinese sectors.