Ireland, stung by an All Blacks try in the first minute, responded superbly and had home fans worried that 101 years without defeat by the Irish was coming to an end.
They opened up a 16-8 half-time lead and defended tenaciously as the All Blacks increased the pressure but the effort took its toll and the Irish wilted in the last 10 minutes.
"They definitely showed their class when it was put to them," said O'Driscoll, who led the British & Irish Lions' tour of New Zealand last summer until injury forced him out.
An outstanding contributor himself with a fine try - his 28th in Tests as Ireland responded to the All Blacks try in the 10th minute - O'Driscoll said: "We have got to play for the full 80 minutes. We missed a couple of first-up tackles.
"But with 20 minutes to go I felt we could push home all the way.
"When we perform as a team and play well, we can compete against any team in the world."
However, he tempered that by saying it was possible to have a 30-point lead against the formidable All Blacks with 15 minutes left and still concede 35.
"We pushed them close this week and we will go close next week," he said, looking ahead to next week's second Test.
The All Blacks, even under pressure, were not afraid to make substitutions to keep fresh legs in the battle, while Ireland were more reluctant to make changes.
It was one of New Zealand's changes, replacement lock Troy Flavell for new cap Greg Rawlinson, who scored the match-winning try eight minutes from the end of the game.
All Blacks coach Graham Henry described the effort by his team as 'rusty' after not having been together since November but he was delighted with the win, and the way the side held together under stern pressure.
Henry said: "We're pretty happy. It was a big ask to come out after seven months against a quality side.
"Hopefully we will get an improvement in the second Test."