Community engagement in higher education has been promoted as critical to fulfilling higher education's responsibility to the public good through teaching, learning, and knowledge generation. Reciprocity and mutual benefit are key principles of community engagement that connote a two-way exchange of knowledge and outcomes. However, it is not clear from existing literature whether community engagement positively impacts communities. This paper presents findings from a dissertation study focused on how campus-community partnership stakeholders define impact and discusses implications for place-based pedagogy. Using grounded theory, the ways community and campus partners defined community impact in a diverse set of campus-community partnerships at two U.S. urban, Jesuit universities that employ a place-based approach to community engagement were explored. Relationships as facilitators of impact and as impacts in and of themselves emerged as central themes that led to the development of the Justice-Centering Relationships Framework. The framework includes two paradigms for understanding community impact in higher education community engagement -- Plug-and-Play and Justice-Centering Relationships -- that are bridged by a reframing process. The framework contributes to and informs the "how" of taking a place-based community engagement approach that leads to positive benefits for community impact, student learning, and institutional change.