The fiercely fought re-run of the 2019 final lived up to its billing as the Dutch enjoyed the ascendancy in the first half on Thursday, before hanging on when the Americans found their groove in the second.
The Dutch struck first through a fine shot from midfielder Jill Roord in the 17th minute at Wellington Regional Stadium and the US went in at halftime trailing in a World Cup match for the first time since 2011.
Horan answered for the four-times champions from a Rose Lavelle corner in 62nd minute, making a great run to the near post to power an unstoppable header past Dutch goalkeeper Daphne van Domselaar.
The Americans had not drawn a World Cup match since 2015 and will rue a slow start to the game as well as an inability to take their chances at the end.
"Even though it didn't finish the way we wanted (it) to finish I thought it was a good match for our team," said US coach Vlatko Andonovski.
"What you saw in the second half is what you're going to see going forward as a baseline."
"These games are battles from the first second to the last ... the only thing you can say is women's football has evolved a lot," said Netherlands coach Andries Jonker.
"Before the match I didn't want a draw - we wanted to win. But after the second half, that's what we wanted because the US were really strong."
The Netherlands broke the early impasse when Lieke Martens pierced the US defence to get the Dutch into the attacking third, and Victoria Pelova cut the ball back for Roord to drill it past goalkeeper Alyssa Naeher from the edge of the box.
The Americans reacted immediately with attempts by Trinity Rodman and Horan that Van Domselaar was able to save, but were given another fright in the 29th minute when Dominique Janssen fired a sizzling shot just over the bar.
The U.S. team, who are in the hunt for an unprecedented third consecutive title, came out in the second half with renewed resolve and got their reward when midfielder Horan equalised just after the hour mark.
Striker Morgan thought she had put them in front a couple of minutes later when she fired the ball into the net from Rodman's pass only to be ruled offside.
Ertz prevented disaster for the Americans in the 80th minute when she got her foot in front of the ball to block forward Esmee Brugts's shot after a well-worked move by the Dutch.
As the US piled forward in search of a winner, Rodman screwed a shot wide of the far post and Sophia Smith had an effort headed off the line by Martens, but the Dutch held firm to secure a point.
