Kogo – who came second in the Great North Run last month – led the half marathon almost from start to finish but had to hold off a spirited attack from Kuma to come home in 1:00:17, two seconds ahead of the Ethiopian.
World record holder Zersenay Tadese of Eritrea was third, almost a minute off the pace.
Kogo’s time was a course record, smashing the legendary Haile Gebrselassie’s 2011 mark by over a minute.
"I'm really happy with the result today," Kogo, 26, said afterwards. "It was a fabulous run for me. At the Bupa Great North Run, I was just pipped to the finish, so to win today in Birmingham is fantastic.
"This course was slightly trickier than the North Run. There is a hill at the end, plus the weather was colder than Newcastle but that makes it a better achievement for me.
"The crowd was amazing, everyone was cheering 'Kogo, go, go' which really pushed me on to get to the finish line."
The women’s race was settled a touch earlier than the men’s, with Portuguese Moreira taking charge with three miles remaining and winning by over two minutes in a time of 1:12:49.
Ethiopia’s Berhane Adere came second ahead of Kenya's Irene Mogaka.
"It's really good to win," Moreira said. "I'm very happy with how the race went although I had a slow first 10km but I picked it up in the second half.
"I'm currently training for the European Cross Country in Budapest and the tough course in Birmingham is good preparation."