The benchmark indices bounced back in late afternoon trade.
The Sensex finished 116 points or 0.41 per cent higher while the NSE Nifty gained 37.25 points or 0.44 per cent to 8,522.15.
The 30-share BSE index had fell as much as 1.1 per cent in the morning session.
Dr Reddy's (+3.7%), Cipla (+3.35%), Hero MotoCorp (+1.34%), TCS (+1.07%) and HDFC Bank (+1.07%) were the top gainers on the Sensex.
All the BSE indices finished in the green. Among the sectoral indices, only metal and consumer durables finished in the negative territory. Health care, oil and gas and FMCG were the top gainers.
Asian stocks hit a six-month trough and the euro stumbled on Monday after a Greek vote against austerity measures endangered its future in the single currency and raised the risk of a full-blown crisis in the euro zone.
IT firms' earnings are expected to be soft amid profit warnings by companies such as Tech Mahindra, Persistent Systems, due to client-specific and cross-currency issues.
"We have been saying for months now, India has nothing to worry about, this is a European problem," said G. Chokkalingam, founder of Equinomics, a Mumbai-based research and fund advisory firm.
Chokkalingam said he expects to see only a marginal improvement in corporate earnings for the quarter ended June.
Asian stocks edged lower early today, as Greece voted against accepting further austerity, increasing the risk of the country’s exit from the euro zone.
Key benchmark indices in Singapore, Taiwan, Hong Kong, Japan, Indonesia and South Korea fell by 0.86 per cent to 5.01 per cent.
Greeks overwhelmingly voted against their international creditors’ conditions for further bailout aid, in a result that could deepen the rift between Greece and the rest of Europe and push the country out of the Eurozone.