When the stumps were drawn, India were reeling at 110/5, requiring another 84 runs to win the game with Virat Kohli (43*) and Dinesh Karthik (18)* still at the crease.
India allowed England to put on board 180 runs, despite having them on mat at 87 for seven at one stage with Ishant Sharma (5/51) and R Ashwin (3/39) troubling the home batsmen in the first two sessions.
His innings followed the 20-year-old Surrey left-arm swing bowler's Test-best return of four for 74 on Thursday.
India will be hoping Kohli, who scored a brilliant 149 on Thursday, can produce another heroic performance as they will need to pull off their highest fourth innings chase in England if they want to take a 1-0 lead in the five match series.
"I had goosebumps listening to the Barmy Army chants and that first hour tomorrow (Saturday) is going to be crucial", Curran told Sky Sports.
England did not have to wait long for their first breakthrough as Broad (2/29) trapped Murali Vijay and then removed Shikhar Dhawan (13) caught behind.
Roaring back Kohli celebrates his brilliant hundred for India
That got the Edgbaston crowd roaring on the bowlers in a manner reminiscent of the raucous cheers that accompanied England legend Ian Botham's celebrated match-winning spell of five for one in 28 balls in the 1981 Ashes Test at the Birmingham ground. Earlier, Ishant Sharma took his eighth five-wicket haul while R Ashwin (3-59) and Umesh Yadav (2-20) shared the other five wickets as the Sam Curran's valiant fight back went in vain.
KL Rahul (13) did not look too comfortable and was removed by Ben Stokes (1/25).
Ashwin struck again when England captain Joe Root was well caught low down at leg-slip by Rahul off a genuine glance. Soon after, he got the wickets of Jonny Bairstow, Jos Buttler and Ben Stokes in the same over and added pressure on the English batsmen.
Middlesex left-hander Dawid Malan arguably "owed" England a big score after dropping Kohli in the slips on 21 and 51.
But Curran, after a couple of fortunate edges and being dropped in the slips on 13, found his form. Sensing closure of the innings, Curran attacked the bowling, hitting sixes off both Sharma and Ashwin, as he reached his maiden Test half-century at a run-a-ball gallop.
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Paul's concerns centered on Judge Kavanaugh's 2015 statement concurring in the denial of rehearing en banc in Klayman v. Joe Manchin (D., W.Va.), one of three Democrats who supported Neil Gorsuch a year ago for the Supreme Court.