Aleh added: "It's going to take a few days. We've tried to treat this like any other regatta, because it's a lot easier to separate ourselves from all the pressure and the hype, and it still seems like just another regatta so far. I don't know how to switch it off. I'm having a few issues with that but I'm sure it will sink in.''
The gold is New Zealand's fourth so far in these Games, and 11th overall, and the first in anything other than windsurfing since Russell Coutts (Finn) and Rex Sellers and Chris Timms (Tornado) won in Los Angeles in 1984. It is also New Zealand's second sailing medal at these Olympics following the silver picked up by Peter Burling and Blair Tuke in the 49er.
This morning's race was virtually won before it began.
New Zealand engaged Great Britain in an aggressive pre-start but appeared to lose out and tacked away to the right-hand side of the course. Great Britain surprisingly allowed them to head off on their own and it proved a critical decision.
Aleh and Powrie built a lead over the rest of the fleet as they found good pressure, with Mills and Clark rounding the first mark a distant last.
"I was surprised when we first cleared, but I think they were a bit stuck,'' Aleh said.
"They would have had to dip a few boats to come back to us. We got out early. I don't know what they were thinking but I guess they were hoping their side would pay but we thought where we were was good.
"As we started going out a lot of the fleet started to tack with us, and we knew we had a great lane. We just had to go fast and keep it simple and hope it worked out, because you never really know.''
The wind conditions only added to that uncertainty. The race started in a steady six knots but died on the first downwind leg which only added to the tension. It would have presented opportunities if Great Britain could have found a wind shift but the task for Aleh and Powrie was improved as race officials shortened the course just before the breeze filled in again.
They didn't really need the help. They raced intelligently, putting themselves in the right places, as the Brits crumbled under the pressure.
The pair embraced soon after crossing the line but didn't really know what to say to each other.
"Maybe a few swear words,'' Powrie admitted.
"I think it was just, 'I think we did it. I can't believe we did it','' Aleh added.
Paul Snow-Hansen and Jason Saunders finished fifth in the men's 470 after they were seventh in the medal race last night (NZT).
The youngsters had only the slimmest chance of picking up a medal - they needed to win the race and hope other results went their way - but the real interest was at the head of the fleet where Australia beat Great Britain in a battle for gold.