The Shots led when Jake Gallagher's cross-shot was prodded in by Scott Rendell.
Summer signing Matt McClure then wound his way past two home defenders, and beat Alan Julian clinically to double the lead with 21 minutes gone.
A relived Bromley finally got their first goal of the season before the break when Joe Anderson centred for Tobi Sho-Silva to head one back.
In the second half, Anderson nearly undid his good work when he headed against his own crossbar from a Jim Kellermann free-kick.
It proved a crucial turn of luck, as substitute Louis Dennis drove past the goalkeeper to level at 2-2 in the 74th minute.
Report supplied by the Press Association.
Match ends, Bromley 2, Aldershot Town 2.
Second Half ends, Bromley 2, Aldershot Town 2.
Blair Turgott (Bromley) is shown the yellow card for a bad foul.
Substitution, Bromley. Connor Dymond replaces Tobi Sho-Silva.
Matt McClure (Aldershot Town) is shown the yellow card for a bad foul.
Substitution, Aldershot Town. Nick Arnold replaces Jim Kellerman.
Substitution, Aldershot Town. Iffy Allen replaces Bernard Mensah.
Goal!  Bromley 2, Aldershot Town 2. Louis Dennis (Bromley).
Substitution, Bromley. Louis Dennis replaces Bradley Goldberg.
Dave Martin (Bromley) is shown the yellow card for a bad foul.
Second Half begins Bromley 1, Aldershot Town 2.
First Half ends, Bromley 1, Aldershot Town 2.
Rob Swaine (Bromley) is shown the yellow card for a bad foul.
Goal!  Bromley 1, Aldershot Town 2. Tobi Sho-Silva (Bromley).
Goal!  Bromley 0, Aldershot Town 2. Matt McClure (Aldershot Town).
Goal!  Bromley 0, Aldershot Town 1. Scott Rendell (Aldershot Town).
First Half begins.
Lineups are announced and players are warming up.
Bromley picked up their first point of the season in a pulsating 2-2 draw at home to Aldershot.