Finke, who led from the outset, set a new world best time of 14min 30.67sec, breaking the previous best of 14:31.02 set by China's Sun Yang in London in 2012.
Italian Gregorio Paltrinieri took silver and Ireland's Daniel Wiffen collected bronze.
Finke, who won gold in both 1500m and 800m freestyle in Tokyo, made his intentions clear from the outset, taking a clear lead in the opening laps.
He was out on his own until Paltrinieri, the gold medallist in this event in Rio in 2016, narrowed the gap around the 850m mark.
The Italian was also swimming at a world record tempo but when it came down to the final four laps, Finke had kept some energy in reserve to ensure he reached the wall 3.88 seconds ahead of Paltrinieri.
"I had a pretty decent lead at about the 300 and I knew I had to keep going. Hopefully try to make the guys hurt a bit trying to catch up with me," said Finke.
"They started catching up with me and I started to get a little worried, but I decided to keep pushing and as long I could keep a little bit of a distance I knew I was in a good shape for the race," added the American.
Despite his impressively quick start to the race, Finke said he had not gone into the race focused on the world record time but became aware he had the opportunity to get into the record books.
"No. I could see the world record line on the board a couple of times. It wasn't like I was trying to see it. I just happened to see it," he added.
"The world's getting faster and I think it's a really good thing. It's a healthy thing for the sport," he said.
Wiffen, who had won a memorable gold in the 800m freestyle ahead of Finke, had said before the race that it would take a world record time to win it.
He was correct but he was unable to deliver it, finishing 8.96 seconds behind Finke.
"It was a record that needed to be off the books. I'm very pleased with Bobby you know, he's a great competitor. everybody's very friendly in the field, which maybe you don't get at a lot of events," said Wiffen, whose win in the 800m had given Ireland their first ever male swimming gold.
"Overall I am very pleased with my week. I was able to secure at least one gold medal so I've got to be very proud of myself," he added.
