It appeared Liam Daish’s side were heading for extra-time at Fratton Park tonight, with the scoreline deadlocked at 1-1.
However, Ben Krauhaus struck a winner three minutes from time to hand Bromley victory.
It means the non-leaguers will face either Swindon or Metropolitan Police in the third round.
Harry Anderson had handed the hosts the lead after 21 minutes with his 17th goal of the season.
Yet Liam Vincent levelled for Bromley just seven minutes later.
The sides couldn’t be separated after that – until Krauhaus’ dramatic intervention to inflict defeat on the Blues.
Pompey: Manderson, Setters, Kaba, Cadman, Bridgman (90 mins Payce), Dawson, Jewitt-White, Dockerill, Lee, Brook, Anderson.
Subs not used: Steward, Chitambo, Simpson, Greenough.