Multi-fin systems, like fish or fish-inspired vehicles, are governed by unsteady three-dimensional interactions between their multiple fins. In particular, dorsal/anal fins have received much attention because they are just upstream of the main thrust-producing fin: the caudal (tail) fin. We used a tuna-inspired fish model with variable fin sharpness to study the interaction between elongated dorsal/anal fins and caudal fins. We found that the performance enhancement is stronger than previously thought (15 % increase in swimming speed and 50 % increase in swimming economy) and is governed by a three-dimensional dorsal-fin-induced cross-flow that lowers the angle of attack on the caudal fin and promotes spanwise flow. Both simulations and multi-layer particle image velocimetry reveal that the cross-flow stabilizes the leading edge vortex on the caudal fin, similar to how wing strakes prevent stall during fixed-wing aircraft manoeuvres. Unlike other fin–fin interactions, this mechanism is phase-insensitive and offers a simple, passive solution for flow control over oscillating propulsors. Our results therefore improve our understanding of multi-fin flow interactions and suggest new insights into dorsal/anal fin shape and placement in fish and fish-inspired vehicles.