Cheltenham led 7-6 after two quarters and 9-7 after three, but York levelled through Jon Lucas and Danny Rippon and snatched the winner just 28 seconds from the end by Paul Floyd.
The other promotion places go to Otter, who defeated Southampton 12-9 thanks to goals by Nikolaos Roussos (6) and Athanasios Mourikas (4); and University of Bristol, 13-9 winners against South Derbyshire.