Sensex rallied over 350 points to scale a fresh intra-day record in early trade on Tuesday, tracking gains in index-heavyweights Reliance Industries, HDFC twins and ICICI Bank, amid a positive trend in global equities, further decline in Covid-19 numbers, and a 10 paise fall in the rupee to 74.20 against the dollar. NSE Nifty too surged 115.05 points or 0.73 per cent to 15,861.55.