East beat his Kenyan rival to the line with a storming sprint down the home straight.
He won in three minutes 37.35 seconds from Chirchir, with Australia's Abdi Youcef third in 3:37.77.
East's team-mate Anthony Whiteman made a bid for victory from 200m out but was overhauled in the home straight, finishing fourth in a season's best 3:38.04.
East surprised himself with his performance and admitted the best he had hoped for was third.
"I have shocked myself. If anything I thought I could snatch a bronze. It's surreal but I am delighted," he said.
"I knew I was capable of winning a major championship but I have been a bit off form and a little bit tired lately, so it is a cross between shock and ecstasy."