Korir won a three-way battle in 2:06:48, more than 30 seconds clear of his fellow countrymen.
Korir, the 2015 Paris Marathon winner, began his decisive attack with five kilometres remaining, and was never significantly threatened en route to the race's dazzling indoor finish area in Frankfurt's Festhalle.
"When the pace dropped after 35-k I put the pressure on - and won," said Korir, who's 2:06:48 performance was the year's eighth fastest. "After having to drop out in the Paris Marathon this spring I was very disappointed. I wanted to redeem myself and I really enjoyed this race."
Kosgei was pleased with his 2:07:22 runner-up finish, a substantial improvement over his previous best of 2:09:50 set in Hannover in 2015.
"I knew from my training that I was in better form than before," Kosgey said. "But it was a surprise to achieve second place."
Kotut, the current Paris Marathon champion, suffered a hamstring injury late in race which ultimately left him out of contention.
"Everything was okay until 35-k when I got the injury," said Kotut, the younger brother of marathon great Martin Lel. "Nonetheless I am happy to have run 2:07 despite the problem."
In the women's race Kenya's Sarah Jebet finished third in a time of 2:27:07 to claim bronze medal.
-Iaaf