There have been Australian cricket supporters in Christchurch this past week and not, word has it, to escape the sense of crisis that has engulfed their team back home. Apparently they were so taken by their experience during the 2-0 series win for their side in March, a return visit was swiftly booked.

Who could blame them? As the red weed of franchise T20 continues its spread and a slightly dystopian landscape forms, this first Test between New Zealand and England has offered a decent counterpoint (even if there have, admittedly, been some depressingly small Test crowds in South Africa and Antigua).

The third day here was another dollop of heavenly bliss, those enticing grass banks packed with spectators young and old who were captivated by the contest. At stumps, as they left to sample the local bars and restaurants, the English among them were eyeing the completion of a 1-0 lead in this series and singing the praises of Chris Woakes.

Yes, Chris Woakes, whose overseas feats in Test cricket have long invited jokes about hiding his passport, and whose name got rather unfairly dragged into the debate about Jimmy Anderson’s enforced retirement. The second of those gripes overlooked the seven-year age gap and solidity Woakes has long provided at No 8 – not that a loose drive to slip in the morning supported this.

Having gone wicketless in the first innings, and then watched Gus Atkinson and Brydon Carse plunder 48 and 33no, respectively, as England posted 499 all out – a 151-run lead built on Harry Brook’s remarkable five-lived 171 from 197 balls – Woakes could have been forgiven for thinking he might be bowling for the continuation of his immediate Test career second time around.

Related: Harry Brook says he was ‘a bit jammy’ to reach 171 after New Zealand fumbles

But 11 years of Test experience – even with that Jekyll & Hyde record home and away – means he is not a flapper. As New Zealand slipped to 155 for six by the close, a lead of four, his figures of three for 39 were central. Bowling a fuller length, and extracting hitherto unseen nip from that unfriendly Kookaburra ball, he sent Tom Latham, Kane Williamson and Tom Blundell on their way.

If the wicket of Latham, caught at second slip for one, levelled things up – next summer’s Warwickshire teammate had held him in the cordon earlier – then the last two will have given him greater satisfaction. The ball was 35 overs old by this stage and while Carse – plus two botched cross-batted shots – had accounted for Devon Conway and Rachin Ravindra, a partnership had formed.

Williamson was steadying things with Daryl Mitchell and England were trying everything, even an attempt to prey on the former captain’s nonexistent ego with the short ball. But it was nous that winkled out Williamson for 61, Woakes resuming from the Botanic Gardens End and beating the inside edge for a bloomin’ good lbw. With Blundell then tickling his first ball – nipping away this time – behind, the Wizard’s spell had turned 133 for three into five.

England wrapped up a 3-0 series whitewash with an emphatic nine-wicket victory over South Africa in the third women’s T20 international at Centurion. Danni Wyatt-Hodge hit an unbeaten 53 as England raced to victory with 51 balls to spare after the spinner Charlie Dean’s three for 26 had helped bowl out the hosts for 124.

South Africa, who were without their captain, Laura Wolvaardt, due to illness, slipped to 45 for five inside the opening eight overs as Lauren Bell and Dean both struck twice. Nondumiso Shangase (31) and Nadine de Klerk (19) put on 52 for the sixth wicket to give the hosts hope of posting a competitive total but the last five wickets fell in quick succession. Dean’s good day continued when she ran out Sinalo Jafta.

Maia Bouchier, who hit five fours and a six in a 21-ball 35, was the only wicket to fall as England raced to their target. Wyatt-Hodge cracked 10 fours and six in her 31-ball knock while Sophia Dunkley finished 24 not out. PA Media

It may be too soon to make predictions about those Australian tourists seeing a 36-year-old Woakes on their shores this time next year, even if Brendon McCullum is ruling nothing out. But one man who looks tailor-made for the trip is Carse. Fresh from a strong start to his Test career in Pakistan, he took his tally in the match to seven by replacing Woakes and knocking over Glenn Phillips for 19.

This was a pretty unfortunate dismissal, induced by a vociferous appeal and shown to be clipping the leg bail by a whisker. Carse, three for 22, was not complaining. New Zealand – though not exactly known for it – could hardly chunter either, having been architects of their own downfall through the eight dropped catches that allowed England, 71 for four on day two, off the hook.

It has been the chief difference here, England’s superior out-cricket exemplified by Atkinson’s athletic low catch at mid-on to remove Conway for eight – heavily scrutinised but deemed to be clean – or young Jacob Bethell holding a swirler with the sun in his eyes to pouch Ravindra on 24. Carse induced both dismissals through the catapult load-up that propels a seriously heavy ball.

So much went back to England’s first innings and a 141-run third morning. Five wickets down, 29 runs behind and with a new ball around the corner, they batted – as is their wont – like they were already heavily in credit. It paid off, Brook ploughing on from his overnight 132, earning a fifth life along the way when Phillips grassed another bullet at gully, and Stokes making a restorative 80, his highest score in 18 months.

Brook averages 89.4 away from home and, this early in their season, New Zealand surfaces suit him nicely. Just as telling was England’s depth with the bat, first Atkinson and then Carse muscling six fours and five sixes between them. Both have the technique to bat as high as No 8, even if the latter’s step to off and hook over fine leg cannot be found in the MCC coaching manual.

Stokes set the aggressive tone, played within himself as the pair cut loose, but looked in good order overall, that bobbing pick-up and flow having returned. There was no century with his mum in the crowd. But the generosity in the city of his birth has been plentiful and anyone tempted by the thought of watching Test cricket in New Zealand should start saving up now.