The BSE index gains 0.29 percent, while the NSE index advances 0.24 percent, turning slightly positive for the month.
Software services stocks are among the leading gainers tracking the weakening Indian rupee.
Infosys gains 1.4 percent, while Wipro gains 1 percent.
Banking stocks also gain on hopes the winter session of parliament kicking off on Thursday will pass bills to liberalise the insurance, pension and banking sectors.
The Indian government's move to allow state-run Life Insurance Corp (LIC) to triple the maximum stake it can hold in other companies to 30 percent also helping banks, dealers say.
State Bank of India gains 1.9 percent, recovering after falling 2.3 percent in November as of Wednesday's close. Axis Bank gains 2.1 percent.