Wilde, the silver medallist in the individual event at the Games, led off for New Zealand on Monday. After a "mediocre" swim, he tangled with French cyclist Pierre le Corre and they and crashed to the ground, according to a Team NZ report.
The incident cost Wilde time he was not able to make up during the rest of the ride or on the run, and after that the Kiwis were always fighting an uphill battle.
The team of Wilde, Nicole van der Kaay, Dylan McCullough and Ainsley Thorpe finished 14th of the 15 starters in 1h 30min 23s - nearly five minutes behind gold medallists Germany (1hr 25.39sec).
There was a photo finish for second place, with officials initially announcing Britain as runners-up but minutes later they announced a switch, with the US getting the silver and Britain the bronze.
Alex Yee, winner of the individual race last week and who anchored Britain to relay gold at the Tokyo Games, gave the defending champions an early lead with a scorching run, with France 40 seconds back in last place after le Corre was brought down on the bike leg.
Georgia Taylor-Brown, also part of the Tokyo gold-medal winning team, was caught by Germany’s Lisa Tertsch at the halfway point but Sam Dickinson handed individual bronze medallist Beth Potter a slight lead.
Potter, Lindemann and a charging Taylor Knibb came off the 7km bike leg together but the German found just enough at the end.
"I believed in myself and I just gave it my all. It's amazing, I can't describe it in words. The team did such a great job and we deserved it so well," Lindemann said.
Tim Hellwig, who kicked off the relay for Germany and was also part of the country's winning team in the world mixed relay championships in Hamburg last year, said his teammate's finish was so exciting to watch.
"We know she has one of the strongest kicks in world triathlon, but you always have to pull it off on the biggest stage, it's always one day and anything can happen but we trusted in her and she did the job in the end," said Hellwig.
France, who had been hoping to upgrade their Tokyo bronze in the event, finished fourth.
- Team NZ and Reuters
