Published: 2019-07-14 20:04:56 BdST
Chasing 242 for victory, Ben Stokes' scintillating 84 not out helped the hosts tie the see-saw contest, forcing the Super Over where more nail-biting excitement unfolded.
Buttler and Stokes took 15 runs off Trent Boult's Super Over without losing their wickets.
New Zealand also scored 15 runs off Jofra Archer's over but England won on boundary count, triggering wild celebrations at Lord's as the hosts capped a stunning turnaround.
Since being unceremoniously dumped out of the 2015 edition of the marquee tournament in Australia, Eoin Morgan's England side have reinvented themselves as a white-ball juggernaut, heading into this World Cup as overwhelming favourites.
Back-to-back defeats by Sri Lanka and Australia in the group stage helped England rediscover the attacking brand of fearless cricket which has been the hallmark of the current team.
They dismantled India and New Zealand to storm into the semi-finals, where they crushed Australia with another ruthless display of all-round excellence.
Sunday's final, England's first since 1992, pitted them against a New Zealand team chasing their own slice of history after spending decades as the tournament's bridesmaids.
Morgan lost an important toss, but Liam Plunkett and Chris Woakes led England's controlled bowling display to restrict New Zealand to 241 for eight on a two-paced wicket.
Henry Nicholls made 55 and Tom Latham chipped in with 47 but lack of significant partnerships hurt New Zealand, who eventually settled for a below-par total.
Nicholls and Williamson put on 74 runs to bolster the New Zealand innings but Plunkett's two-wicket, cross-seam masterclass took the wind out of their sails.
Plunkett dismissed both batsmen just when the partnership was looking dangerous and he eventually finished with 3-42.
Woakes claimed three as well, including the wicket of Latham just when the batsman was looking poised to provide the late charge that could have taken New Zealand past the 250-mark.
New Zealand's new ball pair of Trent Boult and Matt Henry returned determined not to let it become a cakewalk for the hosts.
Henry dismissed the in-form Jason Roy for 10 and Colin de Grandhomme put a struggling Joe Root (7) out of his misery.
England could have been in a bigger hole had de Grandhomme not dropped a waist-high return catch from Bairstow, then on 18.
England were gasping on 86-4 when Stokes was joined by Buttler for a 110-run stand to revive the chase and tie the scores, producing one of the most thrilling matches in the history of the game.