The only goal of the game came in the 59th minute when Ricky Modeste's cross was powered in with a diving header from Joe Healy.
After a quiet opening quarter of an hour, the home side nearly took the lead when Moses Emmanuel evaded a couple of challenges and his shot from seven yards was pushed against the post by Bromley keeper Ross Flitney.
Toby Sho-Silva had the best chance of the first half for the visitors, but his shot from seven yards was blocked and a defender beat Bradley Goldberg to the rebound.
The hosts dominated the second half, but Bromley went close to earning a point five minutes from time when Alan Dunne's header was cleared off the line by match-winner Healy.
Match report supplied by the Press Association.
Match ends, Dover Athletic 1, Bromley 0.
Second Half ends, Dover Athletic 1, Bromley 0.
Ross Lafayette (Dover Athletic) is shown the yellow card.
Aswad Thomas (Dover Athletic) is shown the yellow card.
Substitution, Dover Athletic. Mitchell Pinnock replaces Ricky Modeste.
Ben Chorley (Bromley) is shown the yellow card.
Substitution, Dover Athletic. Aswad Thomas replaces Moses Emmanuel.
Substitution, Bromley. Ryan Hall replaces Bradley Goldberg.
Substitution, Bromley. Blair Turgott replaces Louis Dennis.
Sam Magri (Dover Athletic) is shown the yellow card.
Substitution, Bromley. George Porter replaces Connor Dymond.
Goal!  Dover Athletic 1, Bromley 0. Joe Healy (Dover Athletic).
Second Half begins Dover Athletic 0, Bromley 0.
First Half ends, Dover Athletic 0, Bromley 0.
James Hurst (Dover Athletic) is shown the yellow card.
First Half begins.
Lineups are announced and players are warming up.
Dover got their play-off bid back on track by ending their three-match winless run with a victory over Bromley.