Full-back Ben Smith, who produced a brilliant try-saving tackle on Manu Tuilagi in the first half, Julian Savea and Ma'a Nonu all crossed for the home side, who had trailed 10-6 at half time under the roof in Dunedin.
Fly-half Aaron Cruden slotted a conversion and two penalties, while his replacement Beauden Barrett added a conversion and a penalty for the All Blacks as they stretched their unbeaten streak to 16 games.
Winger Marland Yarde, full-back Mike Brown and Chris Ashton scored tries for England. Owen Farrell, sin-binned for a professional foul midway through the second half, added three conversions and two penalties.
New Zealand had bumbled to a 20-15 victory in the first game in Auckland last week and been under pressure from coach Steve Hansen and captain Richie McCaw to lift their performance.
Both, however, would have been ruing their side's start. All of England's first-half points came in a blistering opening 10 minutes when they denied the All Blacks the ball and the home side fell foul of referee Jaco Peyper, allowing the visitors to kick downfield for attacking line-outs.
"There was a lot of energy in that first 10 when a couple of mistakes put us under the pump," McCaw said of an early Farrell penalty and Yarde's converted try. "We started to slowly get into the game late in the first half and had some momentum going into the second when getting points early put us in control of the game."
Kept in the game by Cruden's two first-half penalties the hosts exploded after the break. Smith finished off a breathtaking counter-attack from 80 metres out before Savea went over in the corner to cap off a 12-point scoring burst inside five minutes. Nonu grabbed the third try when Farrell was in the sin-bin.
Brown scored inside the final 10 minutes to keep England within sight, but by the time Ashton scored his try in the final minute the game was over and the try only made the scoreline look closer than the match was.
"We showed glimpses," was the verdict of England captain Chris Robshaw. "We finished really strongly and started really strongly but lost a little bit of control early on in the second half when we couldn't get hold of the ball.
"It's a results-based industry and we have lost the series, but we have come a long way in the last couple of weeks and hopefully we will get better."
Coach Stuart Lancaster took a more positive view of his team's display. "We had one or two opportunities we didn't take," he said. "We had them under pressure but in the third quarter they were exceptional.
"We got back to 28-27 and that's great character. We played well in the first half but if you kick loosely their back three can kill you. When we look at the tape and the opportunities we missed, we'll be a better side. We were playing a side at the top of their game and went toe-to-toe with them."