In 2013, the Chinese government implemented a two-child policy to increase the country’s fertility rate. However, the persistently low rates necessitated other measures to boost fertility. This study empirically investigated the association between intergenerational support and second-child fertility intention in the Chinese sandwich generation and demonstrated the mediating role of parental burnout and burnout in caring for grandparents. Survey data collected at Time 1, Time 2, and Time 3 included 2939 participants from different regions of China. Before analyzing the data, coarsened exact matching and propensity score matching was conducted to reduce sampling bias. Regression analysis results indicated that intergenerational support has a significant total positive effect on second-child fertility intention. Furthermore, mediation path analysis revealed that parental burnout and burnout in caring for grandparents play significant but opposite directional mediating roles in the association between intergenerational support and second-child fertility intention. Sensitivity analysis using different calipers yielded similar results. These results indicated that second-child fertility intention can be increased among the Chinese sandwich generation with intergenerational support, by mitigating parental burnout. However, intergenerational support did not alleviate burnout in caring for grandparents in the sandwich generation; therefore, formal older adult care policies are required to help the sandwich generation experience lower burnout, while receiving intergenerational support.