Ambrose, who went on to score his maiden Test century and was named man of the match, and Collingwood had taken England from a shaky 136 for five on the first day to 300 for six on the second.
England won by 126 runs on the fifth morning to level the three-Test series. The final Test begins in Napier on March 22.
"You have to give credit to the way Ambrose and Collingwood batted and put together a tough ... partnership that set up the victory for England," said Vettori.
"We let Tim Ambrose get away through some poor bowling and by feeding his strengths.
"When we had them 130 for five we knew we could get into them....it just all comes back to that session, the way we fed his strengths and he capitalised.
"He played very well and probably took the game away from us."
New Zealand, who had won the first Test by 189 runs, were bowled out early on the fifth and final day for 311 at the Basin reserve, chasing a record 438 to win the match.
Brendon McCullum top-scored with a swashbuckling 85 before he was the last man out, hitting Monty Panesar down to long-on where Ryan Sidebottom took the catch in front of the vocal 'Barmy Army' travelling support. Vettori also felt the bowling of the recalled James Anderson on the second day, when he tore the top off New Zealand's batting line-up, had been a major factor in the outcome of the match.
"For us to be bowled out for 198 in the first innings was purely down to him," Vettori added. "He hit the right lengths early on and did a really good job."