Sugarcane bagasse, consisting of cellulose, xylan, and lignin, was chemically treated to generate bagasse samples with continuously decreasing content of lignin. These bagasse samples were hydrolyzed by cellulase and xylanase enzymes, produced earlier by Penicillium janthinellum NCIM 1171 in the same bagasse polysaccharides production medium. The hydrolysis was carried out by using different concentrations of the enzymes at two different temperatures, 30 and 50 °C, taking hydrolysis of Avicel as control. It was found that while the maximum hydrolysis for Avicel was 70% that of some of the bagasse polysaccharides was as high as 95%. The products of hydrolysis were glucose, xylose, and arabinose, as confirmed by high pressure ion chromatography (HPIC). It is interesting to note that arabinose, which constitutes about 10% of the weight of bagasse xylan, could also be released easily by the enzymes. Also, the initial rates of hydrolysis was found to be much higher for the bagasse polysaccharides, and in some cases about 90% of the hydrolysis occurred within 20 h. Amongst all bagasse samples, the sample with (Kappa no. 1.2, lignin content 0.18%) gave the highest degree of hydrolysis at 50 °C. Even the bagasse polysaccharide with Kappa no. 16.8 (lignin content 2.5%) underwent greater extent of hydrolysis than Avicel. Apparently, the delignified bagasse medium appears to be a facile medium for the combined hydrolytic action of the cellulase and xylanase enzymes. Considering that sugarcane bagasse is a waste biomass material available in abundance annually, this methodology can be used to value-add to this biomass to produce sugars, which can be fermented to produce biofuels like ethanol.