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Ten-man Welling failed to build on the midweek win at Boreham Wood after they hit back twice to claim a point at Dorchester on Saturday.
The Wings dropped out of the play-off places despite taking the lead through Lee Clarke as early as the fifth minute.
Dorchester hit back to go ahead through Gary Bowles and Nick Crittenden but Luis Cumbers netted Welling's equaliser on the half-hour.
Healy saw red for retaliation and Chris Flood put Dorchester 3-2 up before half-time.
The Wings lost Jack Oberstellar and Jack Parkinson to injury but snatched a point through Loick Pires before Dorchester were also reduced to 10 men late on.
Welling drop to sixth following Ebbsfleet's 3-1 win at Dover.
Bromley played their part in a bumper encounter in Blue Square Bet South at Hayes Lane against Weston-Super-mare.
Goals from Leon McKenzie, Harry Harding and Harrison Dunk saw them take the honours in a five-goal thriller and keep up their promotion charge in second place.
The Lillywhites fell behind on 15 minutes when Ben Kirk headed in a free kick. Leon McKenzie equalised five minutes later when he calmly slotted home, before Harding made it 2-1 after 32 minutes with a rasping shot from 30 yards out.
But, the scores were level again just before the break when Dean Grubb pounced on some slack defending.
Dunk scored the fifth and decisive goal of the game on 72 minutes when he combined with Tony Finn in a sweeping move through the Weston defence.