The hosts lost six wickets in the afternoon session at Trent Bridge to descend to 124-8 after being put in under heavy cloud cover by India.
But after Shantha Sreesanth, Ishant Sharma and Praveen Kumar had wrought havoc on the top and middle order, England’s Nottinghamshire pair decided a counter-attack was required.
The two natural strokemakers, who faced just four balls together before tea, wrested back the initiative in an evening stand of 73 in only 11 overs.
Broad (64) finished with a second consecutive Test 50, and there was still time for India’s reply to get off to the worst possible start – opener Abhinav Mukund going for a golden duck – on the way to an uncomfortable 24-1 at stumps.
Kumar (3-45) took two wickets in three deliveries in mid-afternoon to end Andrew Strauss’s 98-ball vigil and see off Eoin Morgan for a duck.
England lost Matt Prior cheaply, too, to lurch to 88-6, and then Sharma (3-66) approximated Kumar’s feat with two more wickets in seven balls.
Strauss had helped his team make it to lunch for the loss of only two wickets, at a venue which is renowned for aiding swing and duly lived up to its reputation.
A bouncy surface also played its part in making batting an awkward proposition for all, and India ensured England’s struggle continued by offering few obvious scoring opportunities until Broad and Swann altered the equation.
After the early losses of Alastair Cook and Jonathan Trott, Strauss and Kevin Pietersen dug in for a half-century stand either side of lunch.
Cook survived his first marginal lbw call on one, Asad Rauf just about vindicated when the technology which would normally be used for the DRS system suggested the ball from Kumar probably pitched just outside leg-stump.
But the England opener did not get the luck one run later when Sharma found enough movement off the pitch to beat the forward defence, and Marais Erasmus raised the finger.
Simulated replays suggested the ball would have cleared middle-stump.
Trott’s only scoring shot was a cut for four off Sharma, before he shaped to drive Sreesanth (3-77) and edged some away swing straight into VVS Laxman’s hands at second slip.
India therefore got an early look at Pietersen, England’s hero of Lord’s where a double-century set up their victory to go 1-0 up in this four-match series against the world’s No 1 Test team.
Pietersen climbed into two early pulls at Sreesanth for consecutive boundaries but fell to the same bowler in the first over after lunch, pushing habitually forward and unable to ride the extra bounce as he presented a low catch to third slip.
Nine overs later, Strauss fatally allowed his concentration to slip and edged a loose drive at Kumar high to third slip where Suresh Raina took his second smart catch.
Morgan was then undone by a good delivery, which straightened off the angle to have him lbw on the front-foot defence.
Much therefore appeared to depend on Ian Bell and Prior and sadly for England their wicketkeeper got another good one from Sreesanth, which he edged to first slip.
Bell was dropped by Rahul Dravid at slip off Kumar but the same fielder clung on for a low chance in the same position when Tim Bresnan was turned round by Sharma’s delivery that left the batsman off the pitch, and then Bell wrecked his own hard work by edging an attempted back-cut to be caught behind.
Broad and Swann took over thereafter. The latter eventually fell to an unplayable ball which bounced alarmingly, especially given Kumar’s gentle pace, from just short of a length for an easy catch at gully.
It had a further significant repercussion, too, Swann unable to take the field when India batted because he was instead in hospital having an x-ray on his injured left hand.
Broad, meanwhile, stayed put with James Anderson to flat-bat Kumar straight back over the bowler’s head to complete his 56-ball 50 with his seventh four.
When he was last out, caught in the leg-side deep off Harbhajan Singh, an awkward hour’s batting still awaited India.
Mukund survived for barely a minute of it, spearing a catch to gully off Anderson when he unwisely went after a drive first ball.
As the clouds refused to budge and the floodlights came on, it fell to Dravid and Laxman to avoid further losses against testing spells from Anderson and Broad.
The veterans deserved great credit for battling through.