Late double stuns Sidley
It looked as though honours would finish even, until Sullivan hit a volley which cannoned in off the inside of the near post to give the reigning champions the lead.
The Hillians made sure of victory by adding a second in injury time when Sullivan exchanged passes on the edge of the box before letting fly with a powerful low shot that gave keeper Jon Gardner no chance.
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Hide AdSidley's best efforts were a couple of half chances for Paul Balch and a Kevin Rose drive dragged across goal.
Sidley, who have re-signed wing back Russell Eldridge, visit Division Two outfit Steyning Town in the 2nd round of the RUR Charity Cup on Saturday September 28.