The blue-chip NSE Nifty 50 index ended up 0.71% at 11,521.80, while the benchmark S&P BSE Sensex closed 0.74% higher at 39,044.35.
India's retail inflation of 6.69% in August was lower than a Reuters poll forecast, though it remained above the upper end of the Reserve Bank of India's (RBI) medium-term target for a fifth straight month, which is unlikely to give the RBI room to cut rates at its October meeting.
In domestic trading, the Nifty Smallcap 100 hit a more than six-month high and closed 1.53% higher, while the Nifty Midcap 50 index ended up 0.63%.
Both indexes on Monday had gained 5.4% and 2.1%, respectively, after India's markets regulator on Friday said multi-cap funds must invest at least 25% each in large-cap, mid-cap and small-cap stocks.
The Nifty Bank index, which had fallen nearly 7% in September as of Monday's close, ended 1.65% higher. HDFC Bank Ltd and ICICI Bank Ltd were the top boosts to the Nifty 50, closing 1.2% and 2.2% higher.
Defensive sectors such as IT and pharma also gained, with the Nifty IT index and the Nifty Pharma index closing up 0.63% and 1.93%, respectively.
Consumer goods conglomerate ITC Ltd was the top drag on the Nifty, closing down 0.9%.
Broader world markets rose on positive industrial data from China and optimism around COVID-19 vaccines, with investors awaiting the U.S. Federal Reserve's two-day policy meeting that starts later in the day.
(Reporting by Anuron Kumar Mitra in Bengaluru; Editing by Vinay Dwivedi)