Celtic, who have a game in hand on the table-toppers, benefited from a brace apiece from Mark Benton, Kevin Scott and Neil Richardson.
Cameron Sanderson, Ben Jones and Mike O’Shaunessy were also on the scoresheet.
Celtic are now four points clear of third-placed Wigginton Grasshoppers, who have played a game more.
Skelton, meanwhile, are struggling at the foot of the table having lost seven and won only one of their nine games. They are level on points with second-from-bottom Severus SC, who have only played five games.
The honours were shared in the derby between fierce rivals Hounds and Station.
Gavin Clamp’s first-half strike for Hounds was cancelled out when Station’s Wayne Brooke scored from the penalty spot in the second period.
Station are third from bottom of the table but have only played four league games this campaign, the fewest of any top-flight side.
Marcus Godsall struck four goals and Dave Bradshaw bagged a hat-trick as division two leaders Derwent United beat Hambleton 7-3.
Previously unbeaten Hambleton, who are third, replied with strikes from Wayne Holman, Ian Huddlestone and Kane Snelson.
The home team were 3-0 down at the break and made it 3-1 just after the restart with a goal from Joe Barrett.
Rovers, who won their opening seven games of the season, soon went 4-1 in front, but United’s Andy Manns netted twice either side of a strike by Matty Howden.
Second-placed Albion Vaults beat local rivals Brayton 3-2.
Darren Rollinson scored twice and Dave Hulla once, while fourth-placed Brayton hit back with second-half goals from Craig Waugh and Dale Holt.
Bubwith White Swan beat mid-table foes Selby Olympia 2-1.
White Swan led through first-half marksmen Wes Pears and Tom Robinson, before Luke Lambert snared Olympia’s lone reply.
There were no games in division four, which is headed by Britannia Tadcaster and NUR, on 16 points.
Meanwhile, Tadcaster Magnets were 8-1 winners over visiting Drax in round three of the York FA Sunday Morning Junior Cup, sponsored by Richardson’s Butchers of Woodthorpe.
• York Cubs are scheduled to host Copmanthorpe on Sunday (1.30pm) in a rearranged round three tie in the York FA Junior Minor (Under-13s) Cup. The match was postponed last Sunday.