Bridgefield, who have already qualified, trailed most of the match before reducing the Cheltenham lead to 15-14 in the last quarter. Goals in the last 70 seconds by Solomon Robson and Andrew McAllister steadied Cheltenham nerves.
In Division Three, leaders Solihull defeated Exeter 17-10. Phil Powell scored four of the Midlanders' goals and there were three apiece for Tom Whiting, Peter Farkas, Jordan Elliott and Ben Greenhill.