Shaun Harrad volleyed home his third goal in as many games to give Wrexham the lead in the final minute of a poor first half.
Blair Turgott found himself unmarked in the Wrexham area to fire past Shwan Jalal and bring Bromley level.
But Gerry McDonagh secured Wrexham's win with 10 minutes remaining.
The Dragons, with Dean Keates and Andy Davies in caretaker charge, move up to 14th in the table while Bromley fall to 17th.
Wrexham caretaker manager Dean Keates told BBC Radio Wales: "I couldn't be more proud of the lads.
"They've gone out and shown great character. It was about stopping the rote - the club's not been on a good run.
"It's just positive that we got the result and I'm over the moon for the lads. They've turned it around and got a 2-1 victory they fully deserved."
Match ends, Wrexham 2, Bromley 1.
Second Half ends, Wrexham 2, Bromley 1.
Substitution, Bromley. Reece Prestedge replaces Lee Minshull.
Goal!  Wrexham 2, Bromley 1. Gerry McDonagh (Wrexham).
Substitution, Wrexham. Callum Powell replaces Rob Evans.
Substitution, Bromley. Tobi Sho-Silva replaces Jamie Philpot.
Substitution, Wrexham. Leo Smith replaces Tyler Harvey.
Goal!  Wrexham 1, Bromley 1. Blair Turgott (Bromley).
Substitution, Wrexham. John Rooney replaces Antony Barry.
Second Half begins Wrexham 1, Bromley 0.
First Half ends, Wrexham 1, Bromley 0.
Goal!  Wrexham 1, Bromley 0. Shaun Harrad (Wrexham).
Blair Turgott (Bromley) is shown the yellow card for a bad foul.
Dave Martin (Bromley) is shown the yellow card for a bad foul.
Tyler Harvey (Wrexham) is shown the yellow card for a bad foul.
First Half begins.
Lineups are announced and players are warming up.
Wrexham responded to their shock midweek FA Cup defeat to Stamford with victory over Bromley in the National League.