Having failed to make Sunday’s final, the reigning champions at least salvaged victory in their last match in Mumbai.
Captain Charlotte Edwards saw the side home with an unbeaten 106 as England restricted the White Ferns to 220 for eight and chased them down with three overs to spare and six wickets down.
Edwards, who became the first woman to pass 5,000 runs in one-day internationals, said: “We came here today to win the third-place play-off and to end the tournament on a high is pleasing.
“We’re still disappointed with the overall outcome. But we’ve been thoroughly professional, which is really pleasing.”
For now, Edwards is already looking ahead to the Ashes against Australia in August. If the Aussies win on Sunday, they will travel to England as Ashes, World Cup and World T20 holders.
“We’ve got to go home, rest and refocus,” added Edwards. “The Ashes are something those girls are looking forward to. We’re really disappointment about what’s gone on out here and we can’t wait to take on those Australians come August.”