Morphologically rich languages seem to benefit from joint processing of morphology and syntax, as compared to pipeline architectures. We propose a graph-based model for joint morphological parsing and dependency parsing in Sanskrit. Here, we extend the Energy based model framework (Krishna et al., 2020), proposed for several structured prediction tasks in Sanskrit, in 2 simple yet significant ways. First, the framework’s default input graph generation method is modified to generate a multigraph, which enables the use of an exact search inference. Second, we prune the input search space using a linguistically motivated approach, rooted in the traditional grammatical analysis of Sanskrit. Our experiments show that the morphological parsing from our joint model outperforms standalone morphological parsers. We report state of the art results in morphological parsing, and in dependency parsing, both in standalone (with gold morphological tags) and joint morphosyntactic parsing setting.