The 24-year-old right-back unleashed a fierce left-footed strike from the edge of the box that cannoned home off the underside of the bar for the only goal after 24 minutes.
Peter Murphy and Francis Jeffers both had chances to equalise for Accrington after the break but were thwarted by goalkeeper Stuart Nelson as the Gills moved eight points clear at the summit, although having played a game more than their nearest rivals.
Gillingham nearly took the lead six minutes before Fish's fine effort, with Accrington defender Tom Aldred on hand to clear a Deon Burton header off the line.
Aldred made another good clearance from Danny Kedwell moments later before Chris Whelpdale found Fish, who fired home a spectacular effort from 18 yards.
Kedwell and Joe Martin wasted good chances to double Gillingham's lead before the break while Nelson was equal to a drilled low effort from Murphy and a 25-yard strike from Jeffers afterwards.
- Sports & Recreation
- Francis Jeffers
- Stuart Nelson
- Peter Murphy