Moore ensured his mount was quick out of the stalls and adopted a handy position just alongside the leader, Artic Admiral.
One Pekan coped with Epsom's unique undulations well and rounded the bend travelling strongly.
Moore kicked for home and One Pekan soon surged clear. He idled slightly in front but had enough up his sleeve to win by a length and a quarter.
Roger said: "Ryan has given him a very good ride. He had him in a great position and the horse has stuck on well."
One Pekan (near side) works on the Cambridge Road this spring.