The Kenyan came home in a time of 2 hours 4 minutes 01 second with Britain's Emile Cairess in third.
The race was preceded by 30 seconds of applause for last year's winner Kelvin Kiptum, who was killed in a car accident in February.
Munyao ensured a poignant day ended with another Kenyan victory but only after being pushed by the 41-year-old Bekele.
The Ethiopian, who has won Olympic gold in both the 5,000 metres and 10,000 metres, came close to winning on the streets of the British capital for the first time.
Bekele and Munyao pulled clear of a group including world champion Tamirat Tola but the younger man had the legs in the final few kilometres to win by 14 seconds.
Behind them, it was a great day for the British duo of Cairess and Mahamed Mahamed as they finished third and fourth respectively to close in on a place at the Paris Olympics later this year.
