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Five minutes into the second half Derry doubled their lead when Gareth McGlynn volleyed Alan Murphy's flick over the keeper and into the net.
Derry made it 3-0 in the 54th minute when Mark Farren drove the ball home after O'Flynn had set him up.
Kildare grabbed a consolation goal after 64 minutes. Gareth Cooney sent Shay Zellor clear and the striker gave David Forde no chance from 16 yards.