The Sensex surged 921.30 points to 74,753.85 in opening deals, while the Nifty climbed 254.20 points to 23,417.25.
Brent crude fell 1.62% to $88.92 per barrel after Trump said a deal to end the war with Iran was nearly complete.
InterGlobe Aviation, L&T, Bajaj Finance, Eternal, Trent and HDFC Bank were among the top gainers.