The 22-year-old emerged from the ski jumping stage in second place, jumping 3m further than the rest of the field but lacking the smooth landing of compatriot Jens Luraas Oftebro.
Oftebro's 137.5m jump was perfect and he was rewarded with an eight-second advantage at the start of the 10km cross-country course.
Riiber and Oftebro skied together in the opening section but were unexpectedly caught at the halfway mark by Austria's Franz-Josef Rehrl, known as a jumper rather than a fast skier.
Rehrl even led at one stage but Riiber turned on the power in the closing stages, clocking 26:30.7 for an undisputed eighth World Cup win of the season.
Lincoln Grand Prix