Ethiopia's Feyisa Lilesa claimed the silver medal and American Galen Rupp took the bronze in humid conditions on a rain-slicked course.
Kipchoge, 31, began to split the field after around 30 kilometers, starting with a group of a dozen runners about him that slowly dropped away until he ran the final kilometers alone.
"It was a championship and it was a bit slow so I decided to take over. Maybe it was the rain, maybe not. Everyone wants a medal. I was coming here for gold," said Kipchoge, who has won seven of the eight marathons he has entered, including two London Marathon victories.
Rupp, 30, also made the transition from a short event but did so at the same Games, having finished fifth in the men's 10,000 meters eight days ago.
"I was emotionally drained after the 10K, but I got it out of the system and decided to have an attacking race," Rupp said. "Maybe this is my best event."
It marked the third straight time a Kenyan had claimed a spot on the Olympic podium, following silver and bronze performances in 2012 and a 2008 gold.
Kipchoge's victory came a week after compatriot Jemima Jelagat Sumgong won gold in the women's marathon, marking the first time both races had been won by the same nation.