Foreign investors have bought up to Rs 55,000 crore of Indian equities in November.
Brent crude has fallen toward $90 to $93 a barrel from higher levels.
The rupee closed at 93.69, its strongest level in months.
Banks and autos led the gains on Wednesday.
The Sensex ended at 81,879.40.
Exchanges were closed on Tuesday, November 10, for Diwali-Balipratipada, so Wednesday was the first session after the break, according to 5paisa.
Headlines gave the Sensex gain as 772 points, 773 points or nearly 800 points, while the body reports give only percentages, so the point figure differs slightly by outlet.
The Nifty opened at 25,337.80 and gave up part of its early gains during the day, according to 5paisa.
Thirteen of the 16 major sectors traded higher, according to The Week.
Among Sensex stocks, Mahindra and Mahindra, IndiGo, Trent, Tata Steel and ITC were among the winners, while TCS, Infosys, HCL Tech and Tech Mahindra were laggards, according to The Week.
The Nifty Bank index rose 1.76% to close at 60,792.40, and heavyweight banks lifted monthly gains in the index to 11.2%, according to The Week.
The Nifty PSU Bank index gained 2.91%, according to 5paisa, and about 3%, according to a Business Standard headline.
Nifty Auto rose 2.14%, according to The Week, while 5paisa reports a gain of 1.14%, so the figure for autos differs between the two reports.
Nifty IT fell 0.53%, according to 5paisa, and Mphasis dropped more than 2.5%.
Broader indices also rose: 5paisa reports the Nifty Smallcap 100 up 1.59% and the Nifty Midcap 100 up 0.81%.
IIFL shares rose about 6% after Blackstone was reported to be set to invest Rs 5,000 crore in the company, according to The Week.
Bank deposit growth was over 17% from a year earlier, driven mainly by FCNR-B deposit schemes, according to The Week.
Phiroze Jeejeebhoy Towers, Bombay Stock Exchange, Mumbai (file image), Wikimedia Commons, CC BY-SA 2.0
