City looked a little sharper than the Colemen.
And it showed in the opening half as the visitors had the better openings without managing to finish one off.
But the hosts started the second period much better and could have gone ahead 2 minutes in, but for a great save by City `keeper Gabriel Bajrami, who was brought on at the break.
So, it came as little surprise when Coleshill broke the deadlock in the 58th minute, Max Brogan converting a low cross from 18 yards.
City equalised in the 76th minute when Sean Brain curled a neat effort into the back of the net.
And with 4 minutes to go, Brain beat a couple of defenders before slipping the ball past Paul Hathaway for the winning goal.
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