Moors were looking to make it an all-North-East semi against Gateshead but found Neil Smith`s side just too tough a nut to crack in the tie switched to Darlington`s Blackwell Meadows in an attempt to get it played.
The first half was a cracking affair that kept the 802 crowd on their toes on a chilly evening.
It took only 5 minutes of the opening half for the first goal to arrive when Moors` midfielder Shane Henry found striker Glen Taylor who took a touch, turned and fired an unstoppable drive past Bromley `keeper David Gregory.
But the joy of the home players, bench and fans lasted all of 2 minutes.
A dreadful mistake by the normally so reliable home keeper Dan Lowson, who completely missed his kick to give Louis Dennis the simplest of chances in an open net.
Andrew Johnson came close to restoring Moors` lead from another Henry pass, but his shot was saved by Gregory.
Shortly after the break, the home side`s Rob Ramshaw tried his luck from long range and it took a wicked deflection and almost drops to Taylor, but Gregory pounced on the ball.
But on 55 minutes, Bromley took the lead when Frankie Raymond swung in a deep free-kick which evaded everyone and ended up in the bottom corner of the net.
Dennis almost killed the tie off on the hour-mark but was denied by a decent save from Lowson, and then loanee Brandon Hanlan had another chance to make it 3-1 but failed to connect properly when well-placed.
Spennymoor poured on the pressure near the end with Bradley Fewster and Taylor both going close, but Bromley eventually saw out the tie and celebrated reaching the last four.