In the last few decades, a great deal has been written on the use of sustainable agriculture to improve the resilience of ecosystem services to climate change. However, no tangible and systematic evidence exists on how this agriculture would participate in alleviating impacts on vulnerable rural communities. This paper provides a narrative systematic review (SR) integrated with a bibliometric analysis and a concept network analysis to determine how, in this changing climate, sustainable agriculture can increase the resilience of agrosystems. Our search ranged from the date of the first relevant article until the end of 2018. The results generated demonstrated the following: (a) Only single practices and methods have been studied to assess the impacts on single ecosystem services; (b) Soil quality and health are considered a key indicator of sustainable agriculture; (c) Although the assessed practices and methods were shown to improve the biodiversity of agrosystems, which makes them more resilient to extreme climate events, we are still far from developing interdisciplinary and multidimensional agriculture that integrates all management aspects and generates a full range of ecosystem services. In conclusion, this study addressed the following recommendations for the scientific community and policymakers to orient future research strategies and efforts: (a) The integration of all agrosystem services into sustainable management using an ecosystem-based approach on a life-cycle basis using the Life Cycle Assessment (LCA) method; (b) Improving the scientific understanding of traditional knowledge to facilitate greater synergy and further integration; (c) The unification of assessment methods and indicators for the quantification of impacts; (d) The creation of a platform to share, monitor, screen, and approve assessments and evaluations of sustainable agriculture by region.