New Zealand were bowled out for 284 before lunch, setting England a target of 299 to win, the highest ever to claim a test victory at Trent Bridge. It was a challenging target but England reached it in just 50 overs after Bairstow and skipper Ben Stokes (75 not out from 70 balls) made hay in front of a packed crowd.
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The match set the record for the most boundaries in a test match with 250 in total, including 24 sixes. England were 139 for four at tea, having lost leading batsman Joe Root for three, with the game in the balance.
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But then Bairstow and Stokes ripped the New Zealand attack apart in a devastating fashion, hammering 102 in the first nine overs after the interval. Stokes was hampered by a knee injury, but with Bairstow taking the lead, their partnership was worth 179 runs in 20.1 overs.
Bairstow flew to his century in 77 balls which is the second fastest test century by an England player, one ball slower than Gilbert Jessop's record against Australia at The Oval in 1902.
"It was great fun, one of those things when you get in that mood, just go with it. Do or die, so you've got to do," said Bairstow. The Yorkshireman finally departed to a standing ovation after he was caught behind off Trent Boult, having hit seven sixes and 14 fours.
Stokes and Ben Foakes took care of the remaining 27 runs to soak up the cheers of a crowd that had been given free tickets for the match.
The win was a vindication of the positive approach taken by skipper Stokes and new coach Brendon McCullum who was himself known for aggressive attacking cricket. "Today was set up perfectly for how we want to go about it, run into the danger rather than back away or stand still," said Stokes.
