Wanyonyi clocked a personal best of 1min 41.19sec for victory, Arop taking silver just one-hundredth of a second behind in a North American record.
Pre-race favourite Djamel Sedjati of Algeria claimed bronze with 1:41.50, while Bryce Hoppel was fourth in 1:41.67, a US record.
"This race was tough for me," said 20-year-old Wanyonyi. "I came to Paris, I told myself this race is not easy because it's the Olympics, so I need to run my personal best to win this.
"I felt more pressure because I knew it's not easy. Sedjati is not easy (to beat), he's a tough guy."
Wanyonyi revealed he had had advice from compatriot David Rudisha, who set the 800m world record of 1:40.91 when winning gold at the 2012 London Olympics.
"Rudisha told me yesterday, 'You need to run your race, to run from the start to the finish in front'," he said.
"So I needed to run very fast, that's why I led from the start to the finish line. It was not easy for me."
Wanyonyi was conscious of Arop's fast finishing pace, but said he would not be twice burned, having been pushed into silver by the Canadian at last year's world championships in Budapest.
"If you come from the back, then you beat me over the last 200 metres," Wanyonyi said. "So this time I told Arop, 'Nobody can beat me twice. You need to work hard if you feel to beat me'."
Super-fast race
In a fast race in front of 69,000 spectators at the Stade de France, all eight athletes went sub-1:44, and it was the first time ever that four men in the same race broke the 1:42 mark.
It was a true gun-to-tape effort by Wanyonyi.
At the bell, Sedjati was sixth before falling to the back of the field.
But the Algerian, who became the third fastest athlete in the history of the two-lap race after Rudisha and Denmark's Wilson Kipketer when he won at last month's Paris Diamond League, was not out of it.
He made his move down the far straight as the pace quickened.
But as much as he tried, Sedjati could not catch Wanyonyi and Arop, the pair locked in their own personal battle for gold.
In the end, Wanyonyi dipped for the win ahead of the Canadian, Sedjati just holding off a fast-finishing Hoppel for bronze.
"We've been fighting for this day all year long and we thought we'd timed it right, and I just couldn't be happier with the way I performed," said Arop.
"I've got a huge lifetime best and a silver medal, I can't be upset.
"It wasn't the first time that we've had a finish like that. I knew Wanyonyi was going to have a good last 10 metres and I was just trying to match him."
Sedjati added: "I won the bronze medal, but I wanted the gold medal.
"It was a very fast race. I didn't start very well, but I'm very happy with the medal after the medals from Kaylia Nemour in gymnastics and Imane Khelif in boxing.
"I'm very proud to bring home the third medal for Algeria. It's one of the fastest Olympic finals in history, with four runners on 1:41. I already did my maximum to ensure I got on the podium. I'm happy with this bronze medal."
