Simulation of the polymer extrusion process in fused filament fabrication (FFF) is challenging in terms of both modeling and numerical aspects. When a polymer filament is fed into the nozzle inlet, the polymer is changing from a solid to a liquid phase under the action of heat. The boundaries of the multi-phase polymer body contacts with the nozzle wall before it is extruded out of the nozzle outlet. The extruded polymer strand then contacts with the printing bed, or contacts with other strands in previously deposited strand layers. In such simulation, a significant amount of computational time is spent on the contact computation, especial in a three dimensional setting. Apart from that, the robustness in a contact treatment employed in the computational model usually plays an important role for a convergence of the overall extrusion simulation. A non-smoothness of the contact gap function -- which is used to enforce the impenetration condition -- is often the source of a simulation divergence. Such non-smoothness stems e.g.~from the contact projection from the polymer surface onto the edges of the nozzle wall. In this contribution, we present a robust and efficient contact formulation dedicated to the extrusion simulation in FFF. The efficiency is obtained by modeling the nozzle wall as a rigid analytical surface. Since the nozzle wall in FFF is usually a revolved surface, the three dimensions of the analytical surface can be reduced further to one, representing the profile of the nozzle wall. Such dimensional reduction enables us to develop a fast and robust contact search, given an explicit-analytical function at hand for the nozzle profile. The contact robustness is furthermore enhanced by a smooth isogeometric discretization of the contact surface for the filament boundaries. We consider a Gauss-point-to-segment contact treatment in the presented work. Our contact setting is formulated for both Coulomb friction and a viscosity-induced friction law at the contact interface. The latter is usually required for a liquid state of polymer filament. The robustness and efficiency of our proposed contact treatment is demonstrated by successful simulations of the extrusion process in FFF with a simplified model for polymer filament.