The United States beat the Netherlands 2-0 four years ago to retain the World Cup and are now pursuing a third title in a row, something that has never been done before.
But they were far from their best in front of a crowd of 27,312 in Wellington and fell behind in the 17th minute to a superb strike from midfielder Jill Roord.
Vlatko Andonovski's side grew into the game and struck back just after the hour with a header from skipper Horan, moments after she clashed with her Lyon teammate Danielle van de Donk.
The Americans might have won it after that, but the biggest match of the group stages ended in stalemate and neither side is yet assured of a berth in the knockout phase heading into their final group games.
On Tuesday, the United States face Portugal and the Netherlands play Vietnam, with both expected to win.
US coach Andonovski described Horan's response to the altercation with Van de Donk as a turning point.
"It's a really good example of the leader that she is. She gets fouled, kicked, hurt and obviously it's a very difficult moment," Andonovski said.
"And instead of crying about it, she just goes and makes a statement."
His opposite number, Andries Jonker, was content with the point and called the game a good advert for women's football.
"These games are battles from the first second to the last. The only thing you can say is that women's football has evolved incredibly," the Netherlands coach said.
"We're there, along with the US, and I'm very satisfied with that."
Vietnam out
Portugal defeated Vietnam 2-0 in the other match in the group on Thursday in an encounter between two sides making their debuts at the World Cup.
First-half goals by Telma Encarnacao and Kika Nazareth ended Vietnam's hopes of going any further.
In the final match of Thursday, Australia face Nigeria in front of an expectant sell-out Brisbane crowd.
Having squeezed past Ireland 1-0 thanks to a penalty, the Australians can progress with a victory.
They will have to do it with a dearth of strikers.
Mary Fowler is out of the game after suffering a concussion in training and joins skipper Sam Kerr on the sidelines.
Superstar forward Kerr also missed the opener against Ireland and it remains unclear exactly how long she is out for.
It leaves the Matildas with Arsenal's Caitlin Foord as their only recognised striker.
'Mortal sin'
England are the headline act on Friday when they play Denmark in Sydney.
Denmark coach Lars Sondergaard told his players that it would be "a mortal sin" not to relish playing the European champions.
England's Lionesses failed to sparkle in beating debutants Haiti 1-0 thanks to a penalty but they are still among the favourites to win the World Cup.
With the majority of the Sydney crowd also likely to be behind Sarina Wiegman's side, Sondergaard acknowledged that his team were clear underdogs against "superpower" England.
But he said on the eve of the match: "We hope we can spring a surprise.
"We have settled now, we have our first game (a win) under our belt, that has eased our nerves.
"There's a World Cup every four years, you don't get many of these opportunities in your career," he added.
"It would be a mortal sin not to enjoy it."
Also on Friday, Argentina play South Africa and China face Haiti.