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Two goals at the end of either half ended Welling's unbeaten record in 2010 on Saturday.
The Wings were a distant second to a robust Bath side, who remain on course for the Blue Square South play-offs.
Welling keeper Charlie Mitten (pictured) came to his side's rescue on three occasions in the first half but he could do nothing to keep out Kaid Mohamed's right-foot drive four minutes before the interval.
Welling made a double change at half-time with the introduction of Dean Cracknell and Sam Cutler but it did little to alter the flow of the game.
Mitten somehow saved a deflected effort and then was at full stretch to keep out a potential Andy Sambrook own goal.
Welling's first serious attempt at goal came on the hour when Tony Finn's corner fell to Tom Whitnell, who fired against the bar from close range.
Bath hit the woodwork at the other end before, in the 90th minute, Finn saw his free-kick hit the woodwork. It appeared to be a good save from Bath keeper Ryan Robinson, although referee Lee Vennamore awarded a goal kick.
The visitors wrapped up the points in the fourth minute of stoppage time when Sambrook was caught in possession and substitute Hector Mackie unselfishly set up Dave Gilroy to sweep home.
Bromley swept to a 4-0 victory over Weymouth thanks to two goals in each half.
Ashley Carew set them on their way with a penalty after four minutes and Rob Gillmann added the second midway through the first half.
Richard Butler hit the third after 64 minutes and Warren McBean completed the scoring seven minutes later.
Cray shared a 1-1 draw with Bognor in the Ryman League Premier Division.
Cray fell behind early, but Leigh Bremner equaliser six minutes from time to ensure the points were shared.