Open-graded friction courses (OGFCs) are asphalt paving mixes with a higher number of interconnecting air voids to provide advantages with respect to improved drainage, increased dry/wet surface friction resistance, decreased splash and spray, and reduced aquaplaning. However, binder draindown has been a recurring issue during the manufacture, storage, transportation, and service life of OGFC mixtures. The addition of stabilizers in the form of fiber is often used with OGFC mixes to counteract the draindown. Increasing environmental awareness, the depletion of fossil resources, and the rise of global waste problems have necessitated the use of locally accessible natural fibers as an alternative to expensive synthetic fibers. In this study, the banana fiber obtained from the waste pseudo-stem of the banana plant post-harvesting and the sugarcane bagasse fiber obtained from the post-residual after sugar extraction is explored along with a commercial cellulose fiber to evaluate the draindown characteristics of OGFC mixtures. A cone penetration test and fiber absorption test was performed on the fiber-mixed asphalt binder. The draindown characteristics of 168 combinations of OGFC mixes were evaluated considering various parameters, viz. fiber parameters (types, lengths, dosages), binder dosage, binder types (unmodified binder and polymer-modified binder), and time period. Finally, a statistical analysis was conducted to determine the efficacy of different influencing factors. The best performance was exhibited by banana fiber, which had a dosage of 0.45% and a length of 9 mm, followed by sugarcane bagasse and cellulose fiber. All the input factors were found to be statistically significant.