The first half saw the woodwork struck three times before Adam Cunnington headed Bromley in front from a Bradley Goldberg cross.
Alan Julian was in fine form for the hosts, making three superb saves after the break, the best from Jack Muldoon.
And Goldberg sealed the victory when he rounded Lincoln keeper Paul Farman and fired into the empty net.
Lincoln City manager Chris Moyses told BBC Radio Lincolnshire:
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"I'm not disappointed with the way we played at all. I thought we played well and kept the ball for long periods but were just not ruthless enough at either end.
"The blame will fall on me but I think we put in an honest shift and played some nice football.
"It's a results business and that's all you can say about it. The results will come, maybe not with me but the results will come."
Bromley leapfrogged Lincoln in the National League table with victory in a lively game at Hayes Lane.