BENGALURU, July 21 (Reuters) - Indian stocks rose for a fifth straight session on Tuesday, with financial shares pushing the benchmark indexes to highs last seen in March, as hopes for a COVID-19 vaccine and strong earnings momentum eclipsed fears over surging infections.

The NSE Nifty 50 index rose 1.04% to 11,137.3 by 0351 GMT, while the benchmark S&P BSE Sensex was up 1.13% at 37,839.03, after hitting their highest levels since March 5 in early trade.

Wall Street gained overnight and Asian shares rose further on hopes that vaccines against the COVID-19 disease might be ready by the end of year, following promising early data from trials of three candidates.

Coronavirus cases in India surged to 1.16 million as of Tuesday morning, including 28,084 deaths, according to government data https://www.mohfw.gov.in.

The Nifty PSU Bank Index, which tracks state-owned lenders, was the best performer in early trade, rising as much as 2.7%, after Reuters reported that India is looking to privatise more than half of its state-owned banks.

Bank of India surged 8.7%, while Central Bank of India jumped 18.1%.

Shadow lender Bajaj Finance Ltd advanced 2.1% to a more than four-month high ahead of its quarterly results, and private-sector lender ICICI Bank Ltd rose 2.9%.

IT firm Wipro Ltd led gains on the Nifty, climbing 3.6% to its highest level in more than one year. (Reporting by Chris Thomas in Bengaluru; Editing by Rashmi Aich)