Disclosed is an odor-absorbing, non-dusting porous web material and a method of making the same. The web material includes a porous base web (for example, a fibrous base web, such as a non-woven or paper web) having distributed throughout odor-absorbing particulate (such as zeolite). Alkaline salt or alkaline earth oxide particulate, to better effect removal of acidic malodor, desirably also is distributed throughout the base web, in the final product. The odor-absorbing particulate is bound to the base web (e.g., fibers of a fibrous base web) by a binding system, containing a binding agent. The binding system, in the odor-absorbing web materials, is transparent to the odors so as not to substantially effect the ability of the particulate to absorb odor-causing material. The odor-absorbing web material is formed by dipping a porous base web in a saturant slurry containing the odor-absorbing particulate (the slurry including an alkaline salt or alkaline earth oxide) and the binding agent, together with a surfactant; squeezing out excess saturant slurry from the web; and drying. Also disclosed are two specific uses of the odor-absorbing web material: (1) in personal care products such as catamenial devices; and (2) in packages containing medical materials such as hospital gowns, which materials have been sterilized in the sealed package by gamma sterilization.