Sentiment also got a boost after upbeat US employment data and a halt to a slide in oil eased investor concerns about the global economy.
Gains were broad-based with the BSE midcap index up 1.8 per cent and the BSE small cap index higher 1.9 per cent.
The quarterly earnings season kick-starting with Infosys' results on Friday will set the tone till the central bank's rate decision and the budget in February.
"Sellers are absent in the market. Value-buying coupled with halt in crude oil slide is aiding sentiment," said Deven Choksey, managing director at K R Choksey Securities, adding December-quarter earnings would be muted to steady.
At their day's highs, BSE Sensex gained over 400 points to 27,316 and the Nifty rose 135 points to 8,237, rebounding from their lowest since December 17 hit on Wednesday and after three sessions of losses.
Deutsche Bank set its year-end target for the BSE index at 33,000, citing rising government investment as a key catalyst in 2015. It had earlier set a target of 29,000 for March 2015.
Domestic economy-focused stocks led gains. ITC and ICICI Bank rose 1.9 percent each.
HDFC Bank gained 2 per cent, while Hindustan Unilever rose 2.6 per cent.
Copyright: Thomson Reuters 2015