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Welling produced arguably their worst display of the season as they slipped to a third defeat in four Skrill Premier games on Tuesday.
The Wings showed plenty of effort but they lacked quality and were eventually comfortably outplayed by a Braintree team who still hold hopes of making the play-offs.
Without seven first-team players, Welling named just three substitutes and went with three at the back.
It seemed to be going to plan for the hosts in an evening opening 20 minutes. Defender Alfie Mawson's 30-yard free-kick clipped the top of the bar and skipper Lee Clarke, playing in an advanced role, fed Tobi Sho-Silva but having clipped the ball keeper Nik Hamman, it also missed the target.
At the other end, Welling keeper Lee Butcher produced a magnificent save to deny Kenny Davis' 23rd-minute header but he was powerless to stop the Braintree skipper firing his side into the lead on 35 minutes after Blaine Hudson failed to clear a left-wing cross.
The visitors nearly doubled their lead just before the break but James Mulley, having cleverly worked his way beyond two players, saw his low drive come back off the inside of the post.
The game was effectively settled five minutes into the second half. The players stopped as Hudson was tripped in the box, expecting a free-kick to be given, but instead referee Lee Swabey pointed to the spot for handball as the Wings defender landed on the ball.
Butcher was nearly caught out by Mulley after a poor clearance while the best Welling could muster was a speculative Clarke shot, Sho-Silva's header and Jake Gallagher's near-post attempt.
The Wings - and the watching Dartford boss Tony Burman - will hope for better on Saturday when Welling host Chester at Park View Road.