Jamie Day's side were playing their first league game for 35 days
Welling United moved back into the Blue Square Bet South play-off positions thanks to a 2-1 win over Dartford.
In their first league game since 27 November because of the weather and cup commitments they took the lead through Lee Clarke just before half time.
Luis Cumbers made it two eight minutes into the second half before Dartford pulled a goal back late on.
Welling manager Jamie Day said: "A few were sick at half time but we want to do well and get in the play offs."
He told BBC Radio Kent: "It's all down to the boys, they showed great team spirit again, a few of them were ill, but it shows they're not just here to pick up money."
Dartford boss Tony Burman spoke of his disappointment at how badly his side played, and has threatened changes to his squad.
He said: "I must admit I feel let down. I've got to get things sorted. It wasn't good enough. We tried to get them going but I shouldn't have to do that. You can only go on so long before you make changes. Today it wasn't there."
"If you haven't got heart and passion there's something drastically wrong. We've given them a good chance and it hasn't been working. I'll stick up for any player but today we were poor, it wasn't good enough."
Seven days before their FA Cup third round tie at Huddersfield, Dover needed a late Sam Cutler goal to earn a point in a 1-1 draw at home to Bromley.
Tutu Henriques gave the visitors the lead before the midfielder's late equaliser.
Ebbsfleet United are third after a 1-0 win over Lewes. Substitute Scott Ginty scored their winner. They face leaders Braintree on Monday.
Elsewhere Cray Wanderers moved up to the highest league position in their history, second in the Ryman Premier Division, with a 2-0 win over Hastings. In Ryman South Sittingbourne moved a point closer to the play-offs with a 1-1 draw at Merstham.
Saturday, 1 January
Blue Square Bet South Dover Athletic 1-1 Bromley Ebbsfleet United 1-0 Lewes Welling United 2-1 Dartford
Ryman Premier Division Cray Wanderers 2-0 Hastings
Ryman Division One South Merstham 1-1 Sittingbourne
Monday, 3 January
Blue Square Bet South Braintree Town v Ebbsfleet United Bromley v Bishops Stortford Dartford v Chelmsford City Lewes v Welling United Thurrock v Dover Athletic
Ryman Premier Division Maidstone United v Margate Tonbridge Angels v Folkestone Invicta
Ryman Division One South Faversham Town v Ramsgate Ramsgate v Chatham Town
Ryman Division One North Thamesmead Town v Redbridge
Safety Net Associates Kent League Erith/Belvedere v Beckenham Town Herne Bay v Lordswood Holmesdale v Hythe Town Norton Sports v Deal Town Tunbridge Wells v Erith Town
Tuesday, 4 January
Ryman Division One South Sittingbourne v Chipstead
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