Andy Cook gave the hosts an early lead, heading home Ben Tollitt's corner, before he took his tally for the season to 15 goals by adding his second just seven minutes later.
Tranmere made things hard for themselves when Adam Buxton was sent off in the 56th minute, and Bromley's Brandon Hanlan set up a nervy finish with his 64th-minute strike.
It looked like the hosts would hold firm to claim back-to-back wins, but Jack Holland snatched a point for Bromley with an 88th-minute tap-in.
Report supplied by the Press Association
Match ends, Tranmere Rovers 2, Bromley 2.
Second Half ends, Tranmere Rovers 2, Bromley 2.
Goal!  Tranmere Rovers 2, Bromley 2. Jack Holland (Bromley).
Ben Tollitt (Tranmere Rovers) is shown the yellow card.
Substitution, Bromley. Bradley Goldberg replaces George Porter.
James Norwood (Tranmere Rovers) is shown the yellow card.
Substitution, Tranmere Rovers. Andy Mangan replaces Jack Dunn.
Goal!  Tranmere Rovers 2, Bromley 1. Brandon Hanlan (Bromley).
Ben Chorley (Bromley) is shown the yellow card.
Adam Buxton (Tranmere Rovers) is shown the red card.
Second Half begins Tranmere Rovers 2, Bromley 0.
First Half ends, Tranmere Rovers 2, Bromley 0.
Blair Turgott (Bromley) is shown the yellow card.
Andy Cook (Tranmere Rovers) is shown the yellow card.
Substitution, Tranmere Rovers. Lois Maynard replaces Steve McNulty.
George Porter (Bromley) is shown the yellow card.
Goal!  Tranmere Rovers 2, Bromley 0. Andy Cook (Tranmere Rovers).
Goal!  Tranmere Rovers 1, Bromley 0. Andy Cook (Tranmere Rovers).
First Half begins.
Lineups are announced and players are warming up.
Tranmere squandered a two-goal lead as Bromley rescued a National League draw with a late equaliser at Prenton Park.