Building on the 300+ point gains seen on Monday, the Sensex ended at 18,645, higher by 85 points and the Nifty ended at 5604, up 15 points.
Significantly, the Nifty crossed the 5600 barrier for the first time in 31 months.
The last two trading sessions have been a study in contrast. While Monday's rally was orchestrated by the positive cues worldwide, the current day's session saw a marked divergence between the domestic and global markets.
The Asian bourses had a mixed day; the Hang Seng ended marginally higher, while the Japanese, Korean and Taiwanese markets had a sluggish session.
The CAC, DAX and FTSE were down almost a percent each in mid-day trades after a Wall Street Journal report on the recent stress tests renewed concerns over the sector's health.
And the activity in Dow futures points to a weak start on Wall Street after a prolonged weekend following the Labour Day holiday on Monday.
Markets stage a smart rally
RBI to vet S&P, Dow trading on NSE
US seeks to bail out Dow over Bhopal liability
'Stocks may rise once markets stabilise'
Bhopal: The deception by Union Carbide and Dow