Dutch midfielder Jill Roord fired home a first-half opener to threaten a momentous result in the Group E clash in Wellington.
However, US skipper Horan responded in the second half as the Americans maintained their unbeaten record at the World Cup since losing the 2011 final on penalties to Japan.
"We were a little disappointed with how we played in the first half," admitted Horan.
"But I think we fixed things right away, the pressure we got on and the amount of chances and opportunities that we did."
The result leaves the two teams locked on four points and neither is yet assured of a berth in the knockout phase heading into their final group games next Tuesday, when the US will face Portugal and the Dutch play Vietnam.
Horan's equalising goal from substitute Rose Lavelle's corner came moments after a flashpoint between the US midfielder and her Lyon teammate Danielle van de Donk.
"I respect her so much because that's how it should be, competitive at all times," Horan said.
"Once we got to that tackle, all I wanted to do was score. Heat of the moment, but Rose put in an absolute dime and I got on the end of it."
MORGAN DENIED WINNER
The most highly-anticipated game of the tournament's group phase was vastly different to the decider four years ago in France, which the US won comfortably 2-0 to retain their title.
This time the Dutch had the better of the first half, finding chinks which were also evident in the United States' opening 3-0 win over minnows Vietnam.
Despite dominating the final stages, the Americans couldn't find a winner, producing a hot and cold performance which ends a string of 13 successive World Cup match wins and casts some doubt on their status as favourites to lift the trophy again.
Having opened with a 1-0 win over Portugal, the ninth-ranked Dutch looked like repeating that result when Roord struck smartly in the 17th minute.
The new Manchester City signing – who came off the bench in the Lyon final four years ago – finished with a low drive from the edge of the box to silence thousands of travelling US supporters in a crowd of 27 312.
Seemingly ruffled by a cold, swirling wind, it took until the final third of the game for the Americans to discover their attacking verve.
Horan found space in the box to head home a 62nd-minute corner from Lavelle, the scorer of the second goal in the 2019 final.
It came just moments after Horan needed medical treatment after being clattered to the ground by Van de Donk.
The resurgent US then came very close to unearthing a winner on two occasions.
Striker Alex Morgan found the net only for the offside flag to cut short her celebrations, and a bullet strike from Sophia Smith was kept out by a goal-line clearance from Lieke Martens.