The visitors found their way back into a scrappy first half. Will Whieldon teed up Tom Hill whose header was straight at Terry Smith who then saved a Whieldon free kick after a late challenge on Danny Cocks.
Chasetown began to take charge at the start of the second half and they deservedly took the lead in the 64th minute. A cross from the left found Tom Hill inside the box and he brought the ball under control and drilled into the opposite corner of the goal.
The hosts were reduced to ten men when Michael White saw red for a late challenge inside the Chasetown half.
Skem rallied for a while but Chasetown caught them cold 3 minutes from time with an exquisite lob just under the crossbar from Tom Hill.