Shayne Lavery and Karamoko Dembele were both on the scoresheet against the non-league club at Hayes Lane.
It wasn’t a completely straight forward night for the Seasiders, due the home team asking questions throughout the tie.
Blackpool began the game brightly, with Owen Dale hitting a half volley just over the bar after only two minutes, following a good piece of build-up play from Dembele and Lavery.
The opening goal of the evening quickly followed, as Neil Critchley’s side made the most of their positive start.
On the break, Kylian Kouassi played a pass through to Lavery, who produced a great finish into the top right corner, with the ball going in off the underside of the crossbar.
Shortly after, Albie Morgan and Kenny Dougall both hit efforts off target, as the Seasiders looked to double their advantage.
Down the other end, Bromley were also asking questions, with a couple of moves causing alarm for the visitors.
Just before the half hour mark, Blackpool doubled their lead, courtesy of a moment of brilliance.
Dembele made a superb run into the box, exchanging the ball briefly with Kouassi, before finishing past Grant Smith.
Richard O’Donnell was called into action during the early stages of the second half, with the Seasiders keeper getting down well to stop a shot from distance.
Just after the hour mark, a desperate challenge form Marvin Ekpiteta left the home fans screaming for a penalty, but their protests were waved away by the referee.
Bromley continued to apply pressure onto Critchley’s side, with the visitors proving to be far too passive on the ball.
A late chance landed the way of the home, but they were unable to find the back of the net to set up a tense end to the tie.
Blackpool FC: Richard O’Donnell, Callum Connolly, Marvin Ekpiteta, James Husband, Andy Lyons, Albie Morgan, Kenny Dougall, Owen Dale (82’), Karamoko Dembele, Shayne Lavery (59’), Kylian Kouassi (56’).
Substitutions: Dan Grimshaw, Matthew Pennington, Sonny Carey (59’), Jensen Weir, Jordan Rhodes, Jake Beesley (56’), CJ Hamilton, Dom Thompson (82’), Tashan Oakley-Boothe (82’).