After gyrating 600.70 points during the day, the 30-share index closed 97.30 points, or 0.29 per cent, lower at 33,507.92. It had hit an intra-day high of 33,933.66 and a low of 33,332.96.
Similarly, the NSE Nifty settled 32.85 points, or 0.33 per cent, down at 9,881.15. It touched a high of 10,003.60 and a low of 9,833.80 in the session.
Kotak Bank was the top laggard in the Sensex pack, shedding over 2 per cent, followed by ITC, PowerGrid, M&M, HDFC, Asian Paints and NTPC.
On the other hand, Maruti rallied over 4 per cent. Bharti Airtel, Axis Bank, IndusInd Bank and Bajaj Finance were also among the gainers.
According to traders, border tensions with China, spike in COVID-19 cases and unabated foreign fund outflows weighed on investor sentiment.
Meanwhile, foreign institutional investors sold equities worth a net Rs 1,478.52 crore on Tuesday, provisional exchange data showed.
Globally, bourses in Shanghai, Hong Kong and Seoul ended on a positive note, while Tokyo settled in the red.
Stock exchanges in Europe were trading on a positive note in early deals.
International oil benchmark Brent crude futures slipped 0.83 per cent to USD 40.62 per barrel.
On the currency front, the rupee settled 4 paise higher at 76.16 against the US dollar.