Rhys Oates grabbed a brace and Luke Armstrong was also on the scoresheet as Pools proved just too strong in their eliminator clash.
Dave Challinor’s side, who finished fourth, will now face Stockport next Sunday to try to secure a place at Ashton Gate for the June 20 final.
Hartlepool, backed by a vociferous home crowd, took the lead after 17 minutes when Nicky Featherstone’s ball over the top saw Oates out-pace Bromley skipper Chris Bush and dink the ball over goalkeeper Mark Cousins.
Pools added a second three minutes later as Oates again out-muscled Bush and cut the ball back for Armstrong to beat Cousins via a slight deflection.
And the rampant home side made it 3-0 in the 24th minute when Gavan Holohan nudged the ball to Oates on the edge of the box after neat build-up play and the in-form striker found the bottom corner.
Bush looped in a shot that was headed off the line by defender Gary Liddle with goalkeeper Brad James stranded as Bromley looked to hit back, and a double substitution at the start of the second half paid immediate dividends.
James Alabi had been on the pitch for three minutes when he headed home from a well-worked corner routine.
Hartlepool weathered the storm and were seeing the game out comfortably, only to concede a second goal in stoppage time as Alex Mitchell and home substitute Danny Elliott went for the same ball and a touch took it past James.
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