In this work, a predictive supervisory controller is presented that optimizes the interaction between a diesel engine and its aftertreatment system (ATS). The fuel consumption is minimized while respecting an upper bound on the emitted tailpipe NO_x mass. This is achieved by optimally balancing the fuel consumption, the engine-out NO_x emissions, and the ATS heating. The proposed predictive supervisory controller employs a two-layer model predictive control structure and solves the optimal control problem using a direct method. Through experimental validation, the resulting controller was shown to reduce the fuel consumption by 1.1% at equivalent tailpipe NO_x emissions for the nonroad transient cycle when compared to the operation with a fixed engine calibration. Further, the controller’s robustness to different missions, initial ATS temperatures, NO_x limits, and mispredictions was demonstrated.