It was the fifth successive final for England's Red Roses, but the fourth they have lost to New Zealand.
They led 17-10 at the interval with a penalty try and one by Lydia Thompson plus some excellent kicking from Emily Scarratt, who had been moved to fullback.
But New Zealand, the world's number one side, turned the tables with a dominant display in the second half.
Selica Winiata's try had put the Black Ferns ahead early on.
Natua kept them in contention with another on the stroke of halftime after England had surged into the lead, and she crossed the line again four minutes into the second half, a successful conversion bringing her team level.
After Scarratt's penalty went over via a post, Charmaine Smith and Thompson exchanged tries to leave England 25-24 in front but in almost the next attack Natua completed her hat-trick.
Further tries by Kendra Cocksedge and Winiata set up New Zealand's fifth success in the last six tournaments before England's Izzy Noel-Smith crossed for a consolation.
France beat the United States 33-21 to finish third.
(Reporting by Steve Tongue,; Editing by Neville Dalton)
