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Geophysical studies of the tectonic links between Sri Lanka and India are limited, and consequent paleo‐fit configurations differ and remain uncertain. Here, we present first‐order constraints for an optimum link between Sri Lanka and southern India by using high‐resolution maps of elastic thickness (Te) and crustal thickness (Tc) derived from a flexure inversion method that based on the space‐domain convolution technique for a data window covering integral continental‐oceanic lithospheric setting. We find that the spatial variations of Te and Tc over different crustal provinces in southern India and Sri Lanka agree well with their tectonic classifications proposed by geological studies. Importantly, this study provides much‐needed confirmation of the rifting and associated lithospheric deformation along the mirrored continental margins of India and Sri Lanka and in the intervening transitional lithosphere. The two margins are marked by patterns of low Te and thinned crust, which suggests that an anticlockwise rift (eastward rift) of Sri Lanka away from India resulted in the creation of the Mannar Basin, and a secondary N‐S rifting gave rise to the Cauvery Basin. However, these developments led to a final failed rift, which we attribute to a mechanically strong continental lithospheric bond (a NW‐SE zone of high‐Te and relatively thick crust) that was present in the intervening Palk Strait. We matched the identical zones of Te variations along the two mirrored continental margins and thus obtained a coherent paleo‐fit configuration, and a step‐by‐step evolution of these margins was constructed by using magnetic anomaly‐based paleo‐fit reconstruction models. Key Points: We derived elastic thickness and crustal thickness variations across the continental‐oceanic setting of India and Sri LankaEvidence for anticlockwise rotation of Sri Lanka and evolution of the Mannar‐Palk Strait‐Cauvery BasinsGeophysical results reveal correlation of the mirrored margins of India and Sri Lanka that give rise to their paleo‐fit configuration [ABSTRACT FROM AUTHOR]