Germany's Neugebauer leads Olympic champion Warner after three events of decathlon
Neugebauer, who arrived ranked 13th in the world, had 2,908 points after the 100 metres, long jump and shot put, while Warner scored 2,812 and Canadian teammate Pierce LePage, silver medallist at last year's worlds, was third with 2,784.
World record holder Kevin Mayer of France withdrew after the long jump due to an Achilles injury suffered two weeks ago.
"My feelings are mixed but I will try to manage them," said Mayer, who was in 15th when he pulled out. "Since (the injury), I had eight hours of physiotherapy every day. I was not able to train at all. I knew it was going to be difficult but I tried.
"When I realised my left leg was starting to hurt more and more, I decided to stop. I knew I would not finish the decathlon and I wanted to stop before it becomes a big injury."
Warner led after the 100 and long jump, with the fastest time of the morning in the 100 of 10.32. But Neugebauer, who was 10th at last year's worlds, overtook the Canadian with big personal bests of 8.00 metres in long jump and 17.04m in shot put. His shot put topped Warner's by two metres.
Warner won world silver in 2015 and bronze in both 2013 and 2019, and was in the lead last year in Eugene before pulling up with a hamstring injury in the 400m.
The opening day of the decathlon was set to conclude on Friday evening with the high jump and 400m. Day two on Saturday features the 110m hurdles, discus, pole vault, javelin and 1,500 metres.