The hosts posted 7-201 on the back of 70 from Phil Salt, with the entire India team only just besting the opener's score as they were rounded up for 76.
Archer and Tongue were too hot to handle, both seamers pushing the speed gun past 90mph to scatter the power-packed Indian top order in a match-winning new-ball burst.
Tongue claimed career-best figures in the format of 4-28 and Archer took 3-29, with the innings wrapped up 8.2 overs ahead of time.
It was an emphatic result in Nottingham – eclipsing India's previous worst result in T20s by a massive 45-run margin – and handing the hosts a 2-0 lead with two to play.
India started a difficult day perfectly, winning the toss before Arshdeep Singh delivered a maiden to Salt. It was a red herring, Jos Buttler picking up the pace with 36 of the first 43 runs.
Prince Yadav halted his charge with an inswinging yorker, then added Harry Brook to keep England in check before Salt finally broke the shackles.
Entrenched on 17 from 19 balls at the start of the ninth over, he crashed 53 off the next 25 as a loose over from Varun Chakravarthy eased him into his work.
Harshit Rana struck back with consecutive wickets in the 12th over, Jacob Bethell unable to recreate his match-winning turn from Old Trafford as he hit a skier into the leg side and Tom Banton steering his first ball straight to deep third.
Salt carried on before slashing Axar Patel to backward point.
By then Curran (41no) had picked up the baton and Will Jacks kept the pressure on by flaying two of his first four deliveries into the stands. Two runs off the last ball guided England past the 200 mark.
It proved more than enough as the tourists wilted under a hostile examination. Abhishek Sharma slashed to deep point, 15-year-old Vaibhav Sooryavanshi gloved behind as he took on Archer's bouncer and Ishan Kishan picked out Bethell with a flat pull.
By the time Archer removed Shreyas Iyer and Axar, it was game over at 5-52 from five overs.
India were sprawling, Tilak Varma stumped off Jacks before Tongue dismissed Shivam Dube and Harshit.
Adil Rashid finished things off with two late wickets as India only just beat their lowest T20 total of 74.
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