Livingstone (95no off 78 balls) hit his highest score in ODIs to help the hosts to overcome a top-order collapse on Sunday (Monday AEST) and set New Zealand a target of 227 in 34 overs, after persistent rain had shortened the match and delayed the toss.
"It wasn't quite a rescue mission. We pride ourselves on our depth," said Livingstone, who also scored 52 in the first ODI in Cardiff.
"Lean couple of months but the other day in Cardiff did me a world of good. I just needed one innings."
New Zealand started their chase poorly, losing opener Finn Allen in the second ball of their innings, and wickets continued to fall at a steady pace as David Willey (3-34) and Reece Topley (3-27) took three apiece.
The visitors' main source of runs was again Daryl Mitchell (57), who added a half-century to his ton from the first ODI, but once he departed after holing out to mid-off, there was little New Zealand could do as they were bowled out with eight overs remaining.
Put in to bat earlier on Sunday, England were left reeling at 4-28 in the eighth over as Trent Boult ripped through their top order, taking the wickets of Jonny Bairstow, Joe Root and Ben Stokes.
Captain Jos Buttler (30) and Moeen Ali (33) did well to steady the ship, before Livingstone combined for a 112-run partnership with Sam Curran to rescue England and power them to a competitive total at the Rose Bowl.
"Delighted, from the position we found ourselves in, it's a credit to the way we want to play. It was a fantastic partnership," Buttler said.
"Livingstone and Curran at seven and eight are within their rights to want to bat higher up. Great start for us with the ball and we carried that on throughout the whole bowling innings."
The third ODI of the four-match series will be played at The Oval on Wednesday. The series is crucial for both sides' preparations as they look ahead to next month's World Cup in India.