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Welling's four-match winning run in the Vanarama National League came to an end at rain-soaked Park View Road on Tuesday night.
The Wings had got off to the perfect start with a fourth-minute Michael Chambers header but goals either side of the break from Ali Fuseini and Jack Holland proved decisive for Bromley.
To add to Welling manager Loui Fazakerley's woe, he lost Chambers to injury at half-time and George Porter hobbled off in the final minutes with a hamstring problem.
An entertaining first half saw four good chances, two at each end.
Welling took their first opening, Chambers heading in a deep left-wing corner at the far post inside four minutes.
Bromley should have equalised immediately as Anthony Cook's cross-shot was met by Louis Dennis at close range. But he fluffed what appeared a simple chance and Nortei Nortey was able to clear off the line.
Welling were next to threaten again when Porter got behind after hesitation from Rob Swaine but his right-foot lob went over the bar.
Bromley made him pay minutes later as Fuseini drilled his low shot beyond keeper Tom King from 25 yards to make it 1-1.
Welling had good claims for a penalty turned down on the stroke of half-time when Porter was bundled over in the box but referee Richard Martin waved them away.
The rain got heavier at the start of the second half but the game failed to live up to the pace of the first 45 minutes.
Chances were few and far between until makeshift centre-forward Holland went clean through and slotted past King on 62 minutes.
A head injury to Sam Corne, who was off the field when Bromley equalised, seemed to disrupt Welling as he never regained the control that he had in the first 20 minutes. On-loan Leyton Orient winger Sandro Semedo faded on his home debut after a promising start while Porter, having given Swaine a torrid opening half-hour, lacked support after the break and was often left isolated.
Bromley tucked their two wingers inside to good effect and in Holland they had a much greater attacking threat than Wall offered.
Welling introduced Sahr Kabba and Xavier Vidal but never looked like getting back into the contest, although skipper Ricky Wellard should have done better as his wayward finish failed to match an enterprising run to the edge of the penalty area.
Welling: King, Jefford, Chambers (Osborne 46mins), Porter, Lee, Wellard, Nortey, Lokko, Corne (Vidal 69mins), Harris, Semedo (Kabba 70mins). Subs not used: McEntegart, Williams.
Attendance: 1,127 (359 away).