McIntosh made it look easy aboard her 15-year-old stallion, putting the pressure on Irish rider Shane Breen, who came home with 17 faults.
McIntosh - who is heading home to New Zealand later this month for a new private show at Takapoto Estate in Cambridge - was delighted.
"Who would have dreamed that our day would end with winning a CSIO5* Nations Cup? No words can explain how proud I am of Check In," said McIntosh. "He had such a huge week and to still come out fighting for the team in the jump-off was amazing."
Olympian Goodin, who incredibly had never competed aboard Backatorps Danny V before and the horse hadn't faced a 1.6m course before, described it as a fantastic team effort all week to clinch the result.
"I am struggling to find the words to describe how happy I am," he said. "Danny was amazing to have this result with the little experience he has."
Meech said the victory topped a fantastic week.
"We had to work hard all week together as a team," he said. "Coming in with little build-up plus Bruce riding a new horse wasn't going to be easy. But as a team, we did it.
"We have known each other since we were kids and have been dreaming of this day. It is a very special history-making day for New Zealand."
He thanked the support the riders had received from across the globe.
"I hope this gives something back to New Zealand for hanging in there with us together. This is the best feeling ever."
The Abu Dhabi contest was the first leg of the new 13-round worldwide series.
To get the day's top sports stories in your inbox, sign up to our newsletter here