With England needing to win the Test to square the series, Bairstow posted his fifth century to get his side over the 300 mark on Saturday and Broad ripped through the New Zealand top order to have three for 18 off seven overs at the end of the first session.
When a little shine had gone from the ball and the swing had become less pronounced, wicketkeeper B.J. Watling and all-rounder Colin de Grandhomme were able to combine in an unbroken partnership of 87 which staunched the flow of wickets.
2 - Twice in two Tests Trent Boult and Tim Southee shared ten wickets in an innings. Aggressive at first - he hit three fours from an over from Mark Wood - de Grandhomme settled into a more subdued role and reached his third half century in 100 minutes from 75 balls with six fours.
Bad light stopped play with New Zealand, who lead the two-match series 1-0, closing on 192-6, trailing by 115 runs.
He then dismissed Ross Taylor for the 10th time in Tests, the Kiwi slashing at one that moved late to find Alastair Cook at first slip, before Broad produced a terrific inswinger to the left-handed Henry Nicholls, who departed lbw for a duck after England successfully reviewed.
England face Pakistan in May before they host India for five tests, three one-day internationals and three Twenty20 matches from July.
England had been in trouble at 164 for seven before Bairstow (not out 97) and Wood (52) put on 95 for the eighth wicket.
"We talked as a group about wanting to attack the knee roll and get the brand new ball a touch fuller because we know it flattens out". There will be more twists, as there always are in mid-scoring Tests.
"We've had a couple of meetings in the gap between Auckland and Christchurch, and we're talking a lot more as a team", he said.
Broad finished the day with 4-38 and Anderson with 2-43, less than his efforts deserved. "I felt strong at the crease, I had good pace, my wrist was in a really good position and I got the ball moving".
"I had to improve - and over that short period of time, I think I have". "I was rubbish in Australia", he said, adding that England had the upper hand despite New Zealand's fightback.
"We pretty much ticked all those boxes today as a bowling group, which we're delighted with ..." "The sort that New Zealand want in the battle".