The blue chip NSE Nifty 50 index closed up 0.40% at 15,746.50, while the benchmark S&P BSE Sensex gained 0.44% to close at 52,574.46.
Both indexes had fallen in the first half of the day, as investors continued to digest the U.S. central bank's surprise hawkish turn last week.
However, gains in heavyweight stocks Reliance, Adani Ports and Hindustan Unilever helped both the Nifty and Sensex close higher.
Reliance closed up 0.5%, and was among the top boosts to the Nifty 50. Investors will be focusing on the conglomerate's annual general meeting scheduled on Thursday. Separately, data from India's telecom regulator on Friday showed Reliance Jio added 7.9 million wireless subscribers in March.
Consumer giant Hindustan Unilever closed 1.3% higher for its fifth straight session of gains. Demand for consumer goods and essentials is expected to rise as Indian states continue to relax pandemic-induced lockdowns.
Adani Ports ended 5.3% higher for its second straight session of gains, continuing recovery from a more than 17% fall last week, triggered by a report that said accounts of three foreign investor funds that own stocks in Adani Group companies had been frozen.
Among other individual stocks in Mumbai, state utility firm NTPC closed 3.9% higher after posting higher March-quarter profit. The company was among the top percentage gainers on the Nifty 50.
PNB Housing Finance closed 5% lower after India's markets regulator asked the company to put on hold a share allocation to a clutch of investors led by private equity firm Carlyle Group.
(Reporting by Anuron Kumar Mitra in Bengaluru; Editing by Shinjini Ganguli)