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Welling won in the National League for the first time since mid-October on Easter Monday to end their 23-game winless run.
The Wings are all but down but they aren't dropping down a level without a fight.
They were indebted to goals in either half from Kevin Lokko and Nortei Nortey.
Welling had strong claims for an early penalty somehow turned down by referee Alan Young. Striker Sahr Kabba was bundled over but Young decided there was no foul - even visiting boss Garry Hill conceded afterwards it was a spot-kick.
Three bookings in the first 27 minutes were sandwiched by chances for both sides, as Kabba was denied by keeper Jake Cole and Woking's John Goddard rattled the bar with a 25-yard free-kick.
Welling went ahead on 28 minutes when Scott Kashket's deep corner was headed in at the far post by Lokko.
Woking responded again as Goddard hit the post this time before the loose ball was somehow cleared to safety.
The visitors were back on level terms nine minutes after the break when Matt Robinson broke down the right wing and his cross was turned into his own net by the unfortunate Ian Gayle.
Woking should have been reduced to 10 men when Joey Jones clattered into substitute Kadell Daniel to concede a needless free-kick. But referee Young decided it was not worthy of a second yellow card.
Welling delivered the ultimate punishment instead as Kashket's free-kick was flicked in brilliantly by Nortey, in much the same fashion as Luke Vardy scored for England against Germany.
The hosts nearly added a third goal when Joey Taylor crossed for rookie substitute Luke Saggers but Cole was out smartly to make another stunning stop.
Woking had their chances with Kieron Murtagh heading off target and substitute Giuseppe Sole blazing over from close range.
Welling: McEntegart, Kabba (Daniel 58mins), Wanadio, Kashket (Porter 87mins), Nortey, Gayle, Taylor, Lokko (Saggers 73mins), Corne, Williams, Kargbo. Subs: Bloxsome, Porter, Saggers, Harris, Daniel.
Woking: Cole, Saah, Jones (Arthur 65mins), Murtagh, Goddard (Andrade 42mins), Poku (Sole 74mins), Robinson, Carr, Norman, Robinson, Butcher. Subs: Caprice, Ricketts.
Attendance: 550.