England achieved a straightforward win against New Zealand at Hove on Monday, bowling the visitors out for 80 before chasing down the runs with 37 balls to spare and taking the series 2-1.

Victory was set up by a catastrophic batting collapse from New Zealand, who sunk to 33 for six inside nine overs. A Thomas Becket-esque miracle had saved them at Canterbury, but a second one seemed unlikely, especially when the in-form Sophie Devine was dismissed for a duck.

England’s win came in the absence of their key strike bowler, Lauren Bell, who was rested in anticipation of a big workload over the coming weeks. Dani Gibson stepped up with figures of three for 14, including the big prizes of Devine and Melie Kerr in the same over.

Gibson said that her new bowling action, remodelled to alleviate stress on her back, was working well: “I feel like I’ve been hitting the deck pretty hard in all three games,” Gibson said. “We wanted to perform today under pressure, and we’ve done that.”

Kerr once again chipped up an easy catch into the ring and her form going into the T20 World Cup must now be a concern after scores of one, eight and nought in the series.

The England captain, Charlie Dean, also shouldered some of the bowling load, in the powerplay and at the death, picking up three wickets. Her astute use of DRS again came in handy: she chose to send an lbw appeal against Brooke Halliday upstairs, and reviews showed the ball was drifting on to leg stump.

Dean told Sky Sports: “That was a brilliant win … We learned from the Canterbury to really be ruthless when we were on top. We did that today.”

With such a low target England could afford to be sensible in the chase and wickets fell only when they deviated from that strategy: Capsey was trapped lbw by Nensi Patel and Sophia Dunkley was caught at mid-on trying to loft the ball down the ground.

New Zealand could have made further inroads had Halliday clung on to a tricky catch in the deep when Heather Knight was still in single figures. Instead, a third-wicket partnership between Knight and Maia Bouchier of 35 from 39 balls took England within 10 runs of their target. Knight reverse-swept Melie Kerr to backward point leaving Freya Kemp to finish things off.

Having chosen to bat first in scorching sunshine, New Zealand had placed their hopes for a better start in a different opening combination: Georgia Plimmer was dropped on the back of making consecutive golden ducks, while Suzie Bates was brought back to her traditional place at the top of the order.

But the Bates experiment failed to pay off, with the Kiwi veteran botching a reverse sweep against the ever-reliable line of Linsey Smith; three overs later Izzy Gaze followed suit. Their head coach, Ben Sawyer, said after the match it leaves the reigning world champions with something of a dilemma for the World Cup: who is going to open the batting?

England move on to face a new opponent, India, in another three-match T20 series beginning at Chelmsford on Thursday.