Tele'a touched down either side of half-time as the All Blacks took the series 2-0 and extended their 30-year unbeaten record at Eden Park.
Just like in the 16-15 first Test win at Dunedin, New Zealand had to wrestle back the lead in the second half from a spirited England side.
"Hugely proud of the boys to hold on and win the arm wrestle and finish off a good performance," said New Zealand captain Scott Barrett.
"Test matches certainly challenge your character and we had to dig deep there, right till the last minute."
Fly-half Marcus Smith led the visitors to a 14-13 advantage at half-time after his pin-point cross-field kicks created tries for wing Tommy Freeman and Immanuel Feyi-Waboso.
After a breathless opening spell, the All Blacks took the lead when Tele'a caught the England defence napping from a ruck to dart over for a try.
All Blacks fly-half Damian McKenzie landed the conversion, but England immediately hit back.
Smith kicked wide into the arms of Feyi-Waboso, who stepped inside the defence for a converted try.
New Zealand should have had a second try when Tele'a broke away, but Smith intercepted the final pass to Stephen Perofeta on the England tryline.
McKenzie landed a penalty, but Smith quickly took the kick-off to pin the All Blacks deep in their own half, where they stayed for the next 15 minutes.
McKenzie stroked over another penalty, but England led at half-time after Freeman outleapt Tele'a to haul in Smith's kick.
The England number 10 successfully converted from the touchline .
England started the second-half camped in the All Blacks half and Smith extended the lead to 17-13 with a penalty.
With half an hour left, scrum-half Cortez Ratima came on to make his All Blacks debut when he replaced the dazed Finlay Christie.
The game's momentum swung New Zealand's way when the All Blacks brought on Beauden Barrett.
The twice world player of the year showed his class by restoring the lead for New Zealand when he scythed through a gap to put Tele'a over.
McKenzie missed the conversion, but landed two penalties to pull New Zealand out of England's reach.
The visitors fought until the end with England captain Jamie George denied near the New Zealand line from scoring a potential match-levelling try.
"I think we're a significantly better team than we when we started," said England captain George.
"There's hugely exciting times ahead for this English team.
"We'll welcome them to Twickenham in November, we'll look forward to that."
