The influence of traditional Chinese ritual culture on courtyard spatial sequences is widely acknowledged. However, quantitative analytical methods, such as space syntax, have rarely been applied in studies of ritual–residential space relations. This study uses space syntax, specifically Visibility Graph Analysis (VGA) and axial maps, to conduct a quantitative study of the spatial relationship between ritual and residential areas in Prince Kung’s Mansion. The VGA results indicate a distinct gradient of visual integration, which decreases progressively from the outward-oriented ritual areas, such as the palace gate and halls, through the transitional domestic ritual areas to the inward-oriented residential areas, such as Xijin Zhai and Ledao Tang. This pattern demonstrates a positive correlation between spatial visibility and ritual hierarchy. The axial map results confirm that the central axis and core ritual spaces exhibit the highest spatial connectivity, reflecting their supreme ritual status. More importantly, spatial connectivity is intensified during ritual activities compared to in daily life, indicating that enhanced spatial connectivity is required during rituals. Ritual spaces are characterized by extroversion, high visibility, and connectivity, while residential spaces prioritize introversion and minimal exposure. The deliberately designed ritual–residential architectural spatial sequence of Prince Kung’s Mansion articulates Confucian ideological principles, such as centrality as orthodoxy, gender segregation, and hierarchy. This study visually and quantitatively illustrates the harmony between ritual and residential spaces in Prince Kung’s Mansion. It enhances our understanding of the mechanisms of expression of courtyard ritual cultural spaces, providing evidence-based guidance for functional adaptive transformations in heritage conservation practices. It also offers a fresh perspective on the analysis of courtyard ritual spaces.