Knowledge graph matching is a critical task in data integration that consists of ontology matching and instance matching, i.e., finding correspondences between classes, properties, and instances from different knowledge graphs. Existing approaches for this task often rely on lexical similarities between instance attributes and separate ontology matching from instance matching, leading to suboptimal results. To overcome these limitations, we propose TIM - a tiered iterative knowledge graph matching architecture that leverages the inherent connectedness of knowledge graphs to iteratively find new correspondences. The tiered iterative structure enables the preferred use of high-precision matchers, with recall-oriented matchers running only after the more precise matchers cannot find any new correspondences. We evaluate our approach against several state-of-the-art approaches on multiple real-world datasets. We achieve the best accuracy for class and property matching by incorporating instance information into their matching process and an above-average accuracy for instance matching. Additionally, due to the efficient architecture of our approach, we achieve the fastest runtime for non-trivial baseline systems.