BENGALURU, Dec 1 (Reuters) - Indian shares rose on Tuesday following their best monthly gain since April, with sentiment lifted by data showing a smaller-than-expected contraction in Asia's third-largest economy and broader optimism stemming from hopes for a COVID-19 vaccine.

The NSE Nifty 50 index rose 0.48% to 13,031 by 0454 GMT and the benchmark S&P BSE Sensex was up 0.51% at 44,375.48, while the rupee strengthened 0.66% to 73.57 against the dollar. Indian markets were closed on Monday for a holiday.

The stock indexes had closed out November with gains of more than 11% each, driven by record inflows from foreign institutional investors and news on progress in COVID-19 vaccines.

"India's GDP data has positively surprised markets, there are signs of recovery in key sectors," said Gaurav Garg, head of research at CapitalVia Global Research.

Government data released after market hours on Friday showed India's economy contracted by 7.5% in the September quarter, versus an 8.8% contraction expected in a Reuters poll, amid signs of a pick-up in manufacturing.

"Most of the impact of vaccine-related news has been incorporated by markets, which we saw in the rally in November," Garg said, adding that markets could consolidate in coming days.

Moderna Inc said on Monday it had applied for U.S. emergency authorization for its COVID-19 vaccine, supporting broader Asian shares on Tuesday despite an overnight dip on Wall Street.

In Mumbai, heavyweight IT firm Infosys Ltd was the biggest boost to the indexes, rising nearly 3%.

Pharmaceutical firm Granules India Ltd climbed more than 6% after CNBC-TV18 reported that Carlyle Group Inc was in advanced stages to buy the company for around $1 billion.

Investors are also awaiting monthly auto sales data due later in the day.

The Nifty Bank Index was up 0.27% after gaining nearly 24% last month.

Garg said finance stocks would remain in a tight range until the central bank's policy rate decision due later this week. (Reporting by Chris Thomas in Bengaluru; Editing by Subhranshu Sahu)