This study examines foreign direct investment (FDI)-growth and trade-growth relationships in Bangladesh during three major crises: the economic crisis of 2007–2008, the commodity crisis of 2016, and the coronavirus (COVID-19) pandemic of 2020. The augmented autoregressive distributed lag (AARDL) bounds testing approach and Bayer and Hanck cointegration are employed on time-series data spanning the period 1974–2020. The results suggest that exports have positive effects on economic growth, while imports have insignificant effects in both the short run and long run. Total trade (the sum of exports and imports) has a positive but weakly significant effect on economic growth only in the long run, whereas FDI exhibits a positive effect in both the short run and long run. Although the crises are not found to affect economic growth directly or through trade (i.e., no dampening effect on trade-led growth), they are found to distort FDI-led growth in both the short run and long run. As robustness tests for long-run elasticities, the fully modified ordinary least squares (FMOLS) and dynamic ordinary least squares (DOLS) cointegration techniques are implemented, yielding results similar to those obtained with the AARDL.