Many-body Dissipative Particle Dynamics (MDPD) simulations of binary fluid mixtures imbibing cylindrical nanochannels reveal a strong segregation of fluids differing in their affinities to the pore walls. Surprisingly, the imbibition front furthest into the channel is highly enriched in the fluid with the lower affinity for the walls, i.e., the fluid less prone to enter the pore. This effect is caused by the more-wetting fluid forming a monolayer covering the walls of the pore, while the lesser-wetting fluid is expelled from the walls to the interior of the pore where the higher axial flow velocity carries it to the front. The fluids remix after cessation of the flow. Nonwetting fluids can be made to enter a pore by mixing with a small amount of wetting fluid. The imbibition depth of the mixtures scales with the square root of time, in agreement with Bell-Cameron-Lucas-Washburn theory for pure fluids.