Faversham are only three points behind Ryman League Division 1 South leaders Maidstone after a 1-0 home win over promotion rivals Leatherhead on Tuesday night.
James Peacock, pictured, scored the winner for third-placed Town shortly before half-time.
Sittingbourne dropped out of the play-offs on goal difference following a 1-1 draw with Kent rivals Whitstable at Bourne Park.
Brickies, who fell a place to sixth, took the lead through midfielder Nick Treadwell late in the first half but Danny Williams equalised with 20 minutes left.
Ronnie Dolan scored a 74th-minute winner as Hythe beat Three Bridges 1-0 to draw level on points with Sittingbourne in seventh place.
Folkestone missed the chance to go fifth when Merstham clinched a 2-1 victory in injury-time.
Joe Holland gave Merstham the lead on 17 minutes but Invicta looked set to leave with a point when Josh Burchell equalised eight minutes from time before Adrian Stone won it for the hosts.
Don't miss out, subscribe today. Keep up to date with our newsletters.
A guide for your future. For year 11 students in Kent and Medway. Click here for the e-edition.
Education, Training & Childcare is a special supplement published by KM Media Group four times a year. Click here for latest e-edition.
Get the latest food and drink news, recipes from some of the nation's top chefs plus updates from Kent's vineyards and breweries.
Search in your local area to find your perfect partner in Kent, with FreshStart Dating! PLUS, register for free!.
Find out what's going on in the garden, with Kent expert Lucy Hewett's weekly update.
Buy pictures that you've seen in a KM newspaper, or send in a picture and we will place it on our photo sales website so that you can purchase a super, unique gift.