New Zealand secured a maiden T20 World Cup title, defeating South Africa by 32 runs after a mammoth effort from the all-rounder Melie Kerr, who was named player of the tournament.

After top-scoring with 43 from 38 balls, Kerr was rendered barely able to walk because of cramp brought on by the Dubai heat, but nevertheless she snatched the wickets of Laura Wolvaardt and Anneke Bosch at both ends of the 10th over, turning the match on its head.

It is New Zealand’s first global ­trophy since 2000, and comes off the back of a miserable run of form which included a 5-0 T20 whitewash against England in July. But on Sunday in Dubai everything somehow clicked for the Kiwi underdogs.

Here was vindication at last for the self-styled Kiwi “grandmas” – the 37-year-old Suzie Bates, the 35-year-old Sophie Devine, and the 34-year-old Lea Tahuhu – who have battled for years with barely a sniff of World Cup success (New Zealand last appeared in a World Cup final in 2010) and for whom this was very likely a final chance at World Cup glory.

Bates said: “This means everything to us. When you play team sport you want to be a world champion. We’ve fought our way back to the top. There’s been some dark times when we couldn’t get a win leading into this World Cup and we questioned ourselves as leaders. But Sophie’s been outstanding leading this team.”

Devine said: “I started to let myself dream a little bit last night about what it would be like to hold the trophy up in front of that team. It’s hard to put into words what it means not just for me but for some of the players within this group and for New Zealand cricket as well – it’s been a long time between drinks.”

Kerr was the star, finishing with figures of three for 24, but this was a team effort: Brooke Halliday joined her in a 57-run fourth-wicket stand built on blood, tears but mainly sweat, with plenty of hard running between the wickets.

Then, after South Africa raced to 58 for one after eight overs in pursuit of their 159-run target, Tahuhu piled on the pressure by sending down five consecutive dot balls. A frustrated Wolvaardt tried to hit out, only to be caught on the ring.

Five balls later Bosch – so dominant on Thursday in the semi-final against Australia – feather-edged to Izzy Gaze behind the stumps, and Devine appealed to DRS, overturning the original not-out decision.

Bates proved, as ever, a safe pair of hands at cover, holding on to three catches, while there were also ­wickets for the young spinners Fran Jonas and Eden Carson, and three for the seamer Rosemary Mair, as South Africa’s run-chase petered out.

“Coming to a World Cup, ­everyone starts back at zero and it’s everyone’s game,” Devine said. “The important thing about this group is that it’s not always the person that takes the wickets or the catches – it’s the teamwork, it’s working hard for your mate out in the middle.”

Sent in to bat by South Africa, New Zealand came out all guns ­blazing, ­reaching 50 for one in the opening seven overs before South Africa pegged them back.

Bates celebrated becoming the most-capped player in women’s internationals (334 appearances) by scoring 32, enjoying easy pickings through the leg side, but was bowled by Nonkululeko Mlaba shuffling across her stumps to sweep. Devine then added just six runs before an opportune DRS review by South Africa showed Nadine de Klerk had struck her in line.

But the Kerr-Halliday partnership allowed New Zealand to rebuild, as did some ill-discipline by the South Africans, who sent down 10 wides and three no-balls. They did ­manage to see off Halliday and Kerr in succes­sive overs at the death, but were penalised for a slow over rate which meant they were allowed only three fielders out during the 20th over.

That enabled Maddy Green to send the penultimate ball of the innings sailing over the boundary rope for the first six of the innings: 16 runs came off the over, and the momentum swung firmly back to New Zealand.