"But we had a lot more of the possession during that last quarter but we knew before the game that we would have to defend hard, and while they breached us twice, overall we defended well."
The late try and a fine pressure conversion from the sideline by Tyla Nathan-Wong put New Zealand clear.
"That sort of kick was really the pinnacle for Tyla," he said.
Earlier, the New Zealanders had to face a resurgent French team who had been beaten 54-0 in pool play. The margin was 12-5 in the semifinal.
"We had to keep that pool game in context. France were fourth in Dubai and someday you get those things when we played so well and they were below par but they are improving rapidly and they were after a bit of respect in the semi-final," Horan said.
And the fact that the United States pushed them hard in the quarter-final, dropping the ball over the goal-line at a crucial stage of the game, had showed where the women's sevens game now, he said.
"It's the reality of where we are at. While we have won last year's series, the others are improving and we have got teams chasing us," he said.
Four more rounds in the series remain. The next is in Atlanta in six weeks' time, and six weeks after that the series heads to Canada before a double-header over successive weekends London and Amsterdam in May to complete the series.
New Zealand looked to create their first chance of the final by getting the ball to try scoring Woodman, but Australia had her covered. But in working the ball to the opposite flank they gave Charlotte Scanlan an opportunity which she seized.
However, Woodman was back in the action when demonstrating her individual class by securing a long pass, spinning her way clear and scoring her 12th try of the tournament, the second time she had achieved that milestone.
But the Australians started the second half better and Charlotte Caslick scored in the first minute followed three minutes later by Emilee Cherry to level the scores. A chance to take the lead was lost when Chloe Dalton's conversion attempt rebounded into the field from the goalpost.
As play ranged to and fro, it was finally Woodman who crossed in the eighth minute to secure the win. And New Zealand ensured the pressure was on the Australians in the last moments with Nathan-Wong landing a superb sideline conversion.
The semifinal against France, who New Zealand beat 54-0 on the first day, proved a tight defensive encounter by comparison. After a slow scoring start, New Zealand finally got on the board when Kelly Brazier employed her sidestep to create an opportunity to get over the line.
Then just on the half-time break Kayla McAlister stood up a French defender to cut inside to score with New Zealand leading 12-0 at the turn.
Loose ball however allowed France to score first in the second half as Shannon Izar picked up the ball and dived over. There was no more scoring but the New Zealand defences withstood the best French efforts.
The New Zealanders survived a scare from the United States in their quarter-final.
They opened the scoring when captain Sarah Goss ran through a hole to score but the Americans caught them by surprise with some helter-skelter, but accurate, passing moves to create a chance for Lauren Doyle to score.
However, New Zealand regained the initiative with quick tries to Charlotte Scanlon and McAlister to go to the break up 21-5.
More frenetic passing plays in the second half resulted in the USA scoring first, out wide, when Jessica Javelet touched down. Then followed that with Kristen Thomas scoring beneath the posts after a New Zealand mistake.
Then with a sensational upset looming Thomas crossed the line after a superbly-timed pass but lost the ball before scoring.
New Zealand recovered when Woodman scored the 60th try of her career for a 28-17 win.
Australia qualified for the final with a 29-10 quarter-final win over England and then had to come from 5-7 down to beat Canada 12-7 in their semi-final.
