Brendon McCullum (69) threatened to delay England significantly in this middle match of three, with a forecast for increasingly heavy rain a major complication for the remainder of the contest.
But Broad led an admirable performance from the tourists' pace attack to bowl out the Kiwis for 254 in reply to 465 all out.
Then after enforcing the follow-on, in 33 more overs England had to settle for just Hamish Rutherford's wicket as Peter Fulton and Kane Williamson guided the hosts to 77 for one at stumps.
Broad, without a wicket before succumbing to injury during England's historic series victory in India before Christmas, trebled his winter Test tally at the Basin Reserve ground.
Trying to pinpoint the reasons for the loss and recovery of his form, he said: "I only really struggled in India. Up until then, taking 40-odd wickets in the year was pretty good.
"I hurt myself in the warm-up game and probably should have gone home then."
"I've probably been due some wickets, and it's good to have been able to do it," he said.
"Today, it was just my day to get the nicks.
"Probably the second new-ball wickets were the most important, obviously with the follow-on being so close."
He was in no way flattered either by his figures after a fine display of swing and seam bowling on a pitch still offering him and others minimal assistance.
Broad and James Anderson took two wickets in four balls in the first half-hour this morning - and then after McCullum dominated a century stand with BJ Watling (60), Steven Finn finally saw off the New Zealand captain and Tim Southee in successive overs with the old ball.
McCullum's limited-overs runs kept the Twenty20 and one-day international series competitive, before England twice prevailed 2-1 on this tour.
He was at it again too in last week's drawn first Test in Dunedin, with a typically belligerent 74, and here took his half-century count to five in succession and six in his last seven innings.
England's initial breakthrough today was a bonus, achieved in unlikely circumstances.
Williamson drove a full-length ball back at the perfect height for Broad to hold a sharp return chance just to his left in his follow-through.
It was a mode of dismissal which could hardly have been part of the plan.
But as the previous night, when Broad took two wickets in two balls, England again cashed in quickly - thanks to Anderson this time, who got one in the right place to Dean Brownlie and hit him deep in the crease with a delivery which nipped back.
The height of impact gave him hope on the Decision Review System, but simulation narrowly vindicated Asad Rauf's lbw decision.
Broad had already beaten McCullum's outside edge first ball, and did so again with a very good out swinger three overs later before also snaking one back to hit him on the pad just outside the line of off stump.
In between, though, New Zealand's danger man cracked Broad for two back-foot fours through the off side and then pulled him for a mighty six over square-leg.
By lunch he was past 50, from 64 balls, having hit six fours and that six.
Three more boundaries followed from him at the start of an afternoon session which saw McCullum escape a marginal lbw review against Anderson - who also had Watling dropped on 21 by Jonathan Trott at second slip.
Finn was soon back in the attack instead, in tandem with Monty Panesar to give Anderson and Broad a rest for exertions still to come, and it was he who brought the follow-on back into the equation.
McCullum fell as Watling ought to have, safely held by Trott, and Southee hooked Finn to Broad at long-leg.
But it took another 12 overs, until the third with the second new ball, before another very good delivery from Broad had Watling edging behind - leaving the Kiwis with 26 more runs to eke out from numbers nine to 11 to avoid having to bat again straight away.
That target was halved by the time Broad bagged his fifth wicket, taking one away off the pitch to have the left-hander Neil Wagner also caught behind for a duck.
Then in his next over, England's man of the moment finished the job when the hapless Trent Boult was last out via an inside edge to Matt Prior - leaving a defiant Bruce Martin unbeaten on 21.
Given the predicted advance of Cyclone Sandra tomorrow, England had no sensible option but to enforce the follow-on.
But it was no surprise that they then found progress slow through the evening session, with conditions still very much in the batsmen's favour and a hard-worked attack in which Anderson was soon showing distress signals.
A moment of brilliance from Ian Bell at leg slip, immediately after being positioned there by Alastair Cook, brought a one-handed diving catch to see the back of Rutherford in Panesar's first over.
England's only other opportunity was another half chance given by Williamson on one, which Prior could not take at full length down the leg side off Finn.
Records tumbled in Mohali as the opener Shikhar Dhawan led India's superb response to Australia's first innings of 408 in the third Test.
The left-hander's boundary-laden onslaught captured the crowd's attention even more than his distinctive handlebar moustache as he took just 85 balls to reach three figures.
It was the fastest recorded century on Test debut, beating the 93-ball mark set by the West Indies' Dwayne Smith against South Africa in 2004.
By the time Dhawan closed on 185 he had made the highest score by an Indian debutant, beating Gundappa Viswanath's 137 back in 1969, while he and Murali Vijay, whose unbeaten 83 went almost unheralded, set a record opening partnership on this ground.
A stumps score of 283 without loss served to overshadow the morning heroics of Australia's Mitchell Starc, who was dismissed one run short of a deserved hundred, and Steve Smith (92).
The pair put on 97 before Smith, who had looked comfortable throughout, was tempted out of his crease by Pragyan Ojha and stumped by MS Dhoni.
That just encouraged Starc to attack more, though, claiming boundaries almost at will off Ojha and punching a short ball from Ravichandran Ashwin for four.
But, needing one for his century, he played and missed twice outside off stump at Ishant Sharma, then made contact the third time and Dhoni snaffled the catch.
He could manage a wry smile as he trudged off the pitch with his highest first-class score - sportingly congratulated by Sharma - and the rest of the players followed soon after as last man Xavier Doherty was lbw to Ashwin.
Dhawan made a blistering start in the Indian reply and took an early liking to the medium pace of Moises Henriques, with two boundaries off his third over and two more in his next.
That took him to 40 from 39 balls, 36 of them in fours, and he moved past 50 at better than a run a ball with three more boundaries off the spinners Doherty and Nathan Lyon.
The more restrained Vijay joined in the fun with two sixes in an expensive Lyon over and, when Starc's return was greeted in typical style by Dhawan, the century partnership was on the board inside 22 overs.
Even though the boundaries dried up slightly with three figures approaching, Dhawan continued scoring quickly, although he was fortunate to see an edge through the slips find the rope to take him to 98.
As if his innings was not remarkable enough, he reached his ton with a five when he dived to complete a risky single and the throw at the stumps flashed past for four overthrows.
Dhawan hit 21 fours and his innings was the fourth-fastest Test century by an Indian batsman, a list headed by 74-ball tons from Kapil Dev and Mohammad Azharuddin.
Vijay was unbeaten on 42 at tea and got his moment in the spotlight in the fifth over of the evening, clipping Lyon for two to bring up a 103-ball half-century. He had hit Peter Siddle for his fifth four in the previous over, to go with his two sixes.
Dhawan hit what remarkably was his first six - and almost his first aerial shot - when he lofted Lyon into the sight screen despite being deceived in the flight.
The 200 partnership came up with three Dhawan boundaries in one Starc over and Lyon then suffered the same fate before Dhawan reached 150 from 131 balls.
Smith could not stem the flow of runs, twice disappearing for back-to-back boundaries, and the punishment continued for all Australia's bowlers until the close when Dhawan emerged from a deserved mass of handshakes for a triumphant, moustache-twirling walk to the pavilion.