England led 22-14 late on but replacement fly-half Damian McKenzie's penalty and Tele'a's second try of the match helped leave New Zealand two points ahead with three minutes left.
England substitute fly-half George Ford, who had hit the post with a 79th-minute penalty -- his first goal-kick of the game -- then missed what would have been a winning drop-goal with the last kick of the match.
The veteran playmaker, winning his 97th England cap, had also gone too high in the tackle when Tele'a crossed for a second time, with McKenzie converting.
"I didn't think we had that in the end," New Zealand No 8 Ardie Savea told TNT Sports.
"We got lucky with the penalty kick, but rugby is a game of fine margins and we will take it," he added after a morale-boosting win for New Zealand, beaten by South Africa in the 2023 World Cup final, following three defeats in six games during this year's southern hemisphere Rugby Championship.
"That game could've gone either way but for us to stay in it and defend the goal-line like that, I'm very proud of the boys.
"England's pack were bringing line speed and they were putting big shots on us."
Defeat in their November opener was another frustrating loss for England, with Steve Borthwick's men beaten in several close games since the World Cup -- including 16-15 and 24-17 losses in New Zealand in July.
Saturday's reverse was particularly tough on fly-half Marcus Smith, who kicked 17 points and made the interception that led to England's lone try through winger Immanuel Feyi-Waboso.
"We gave them (New Zealand) a window to get back and they did it," Borthwick told reporters as he cited the All Blacks' greater experience and recent time together as reasons for the defeat.
"They had 10 players from the World Cup final and had more caps in their 15 than we had in our 23," added the former England captain.
"New Zealand are a quality side and since we last played together they have had seven Test matches and been together three months."
The All Blacks made wholesale changes to the team that thrashed Japan 64-19 last week, with Scott Barrett captaining a side where his brothers Beauden and Jordie lined up alongside each other at fly-half and inside centre for the first time in a Test.
Home playmaker Smith gave England a fifth-minute lead.
But New Zealand hit back four minutes later when, after a neat reverse pass from flanker Wallace Sititi out of a tackle by England full-back George Furbank, Tele'a went over for a try on the blindside as he out-matched England prop Ellis Genge.
Beauden Barrett converted and New Zealand led 7-3.
England, however, reduced that gap to just a point with a Smith penalty.
- Barrett class -
New Zealand pulled clear in the 28th minute when Beauden Barrett's superb inside scissor-pass released full-back Jordan who ran in from some 30 metres for his 36th try in just 38 Tests.
Beauden Barrett's conversion put New Zealand 14-6 ahead before another Smith penalty cut the deficit.
England flanker Chandler Cunningham-South's thumping tackle on Tupou Vaa'i which led to a knock-on roused a crowd of over 81,000.
From the ensuing scrum penalty, Smith was on target with a 47-metre effort.
The second half was just five minutes old when Smith picked off a Cortez Ratima pass deep in his own 22 before sprinting clear of Jordan and linking with Furbank, who in turn released Feyi-Waboso.
Beauden Barrett thought he had scored a breakaway try but the score was ruled out on review for a deliberate knock-on by winger Caleb Clarke.
Smith's penalty left England 22-14 ahead and in sight of just a ninth win in 46 Tests against New Zealand.
But McKenzie's penalty, following a 'no-arms' tackle by No 8 Ben Earl, sparked the All Blacks' revival.
New Zealand next play Six Nations champions Ireland in Dublin on Friday, with England facing Australia at Twickenham a week on Saturday.
