England secured a nervy final-over six-wicket win against New Zealand at Canterbury on Thursday, securing the series 3-0 with two matches left to play, despite Jon Lewis’s controversial decision to rest the captain, Heather Knight.

Alice Capsey struck a career-best unbeaten 67 after successfully having an lbw decision against her overturned by DRS on 40 – reviews showing it would have missed leg stump – while New Zealand were made to pay for errors in the field. They put down Amy Jones on 11 and 18 before a misfield by Fran Jonas at deep third sent the ball over the boundary rope to see England home with four balls to spare.

Capsey said that a total break from cricket before the series spent with friends and family had put her in the right headspace to perform at her best: “I’ve been under the spotlight for the past three years and it’s taken its toll a little bit,” said the 19-year-old. “I’ve taken a step back this year and gone, what’s the best option for me to go out on to the pitch and perform? I’m prioritising myself a little bit more. Not listening to the outside noise as much and focusing on what matters to me. I feel the most calm and controlled I’ve felt in a very long time.”

Six matches into the tour, New Zealand finally made England fight for their win: the hosts had nerves jangling at nought for one after Maia Bouchier was trapped lbw by Hannah Rowe for a first-ball duck, and then again mid-innings as the left-arm spinner Jonas took two in two and the required rate crept above 10.

Related: Alice Capsey fires England to rain-hit T20 win over New Zealand

Sophie Devine and Melie Kerr turned the screw at the death, combining to run out Jones with 22 needed from the final 15 balls, but Freya Kemp smashed consecutive boundaries off Leigh Kasperek to ensure England needed just five runs from the final over.

Earlier, Devine had muscled her way to an unbeaten 58, including two huge sixes and consecutive fours from the last three balls of the innings, as New Zealand added 41 runs in the final three overs.

Her fellow Smash Sister Suzie Bates struck a glorious-looking 38, becoming only the third woman to pass 10,000 international runs, and the first to achieve the feat for New Zealand – only India’s Mithali Raj and England’s Charlotte Edwards have previously achieved the milestone.

But in between times Sophie Ecclestone took four for 25 – including breaking up Bates’ fruitful 52-run powerplay partnership with Melie Kerr with a double breakthrough in the eighth over – as New Zealand’s innings flopped about like a dying fish.

England had continued their revolving-door one-eye-on-Bangladesh selections, with seamers Kemp and Dani Gibson handed the chance to bowl in the powerplay and at the death – the former with strapped shoulder, the latter with strapped knee.

But the most bizarre aspect of England’s World Cup what-if scenario planning was “resting” Knight. If the move was supposed to reassure England that they could cope perfectly fine if their skipper comes down with a nasty case of Delhi Belly in Bangladesh, then it backfired. Nat Sciver-Brunt may formally be England’s vice-captain but expecting someone who rarely captains any team (domestic, franchise or global) to be able to switch it on and off at the drop of a hat is just not fair on that player.

With England’s run chase hanging in the balance at 66 for two in the ninth over, needing 76 from 67 balls, Sciver-Brunt was pinned lbw by Jonas for a first-ball duck. Worse, she failed to send the decision upstairs, despite Hawk-Eye later showing that it would have missed leg stump. Meanwhile, where was Knight? On air, live on Sky, discussing the match she should have been playing in.