The fall in crude oil futures was mostly due to trimming of positions by traders, in line with weak global cues, analysts said.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell by 0.07 per cent to 97.91.
Tech Mahindra, Yes Bank, Infosys, Vedanta, M&M and L&T too fell up to 1.13 per cent.
US crude inventories rose by 4.3 million barrels in the week ended Nov 1 to 440.5 million barrels.
Forex inflows through Bajaj Finance share sale to qualified institutional investors helped the rupee hold strong, said analysts.
After swinging 413 points during the session, the 30-share Sensex settled 53.73 points, or 0.13 per cent, lower at 40,248.23.
Gold is trading at Rs 39,213 per 10 gram on Tuesday on rupee appreciation and selling in global markets.
Crude oil for delivery in November was trading lower by Rs 46, or 0.14 percent, to Rs 4,004 per barrel in 27,004 lots.
By 2023, up to 30 per cent of world news and video content will be authenticated to counter deepfake technology, the report said.
Rupee is trading at 70.73 against dollar, following increased selling of the American currency by exporters and banks.