An injury-time equaliser by Brad Lethbridge kept Bognor in the FA Trophy.
His late strike clinched a 2-2 draw and earned a replay - which will be at Nyewood Lane on Tursday evening - after the Bostik south central side looked set to knock them out at the first hurdle.
Bracknell led twice through first-half goals by Liam Ferdinand and James McGlurg but Jimmy Muitt and then Lethbridge dragged Bognor back into it.
Had Bognor lost it would have been the third time this season they'd lost a cup tie to a lower-division side, so that's one unwanted statistic avoided.
Elsewhere, in the Southern Combination premier Chichester City are still top after a comfortable 3-0 win at home to Crawley Down Gatwick in which the returning Josh Clack, and Matt Axell, were among the scorers.
Pagham also enjoyed a vital home win - George Gaskin scoring to see off Horsham YMCA 1-0.
In the SCFL division one derby at Selsey, Midhurst won 1-0. Sidlesham got back to winning days, beating Storrington 3-1 with an Alfie Bunker goal and two fron Morgan Forry doing the damage.
But it was a bad day for Bosham - they lost 10-0 at Rustington in SCFL division two.
We'll have a full Bracknell v Rocks report on this site later and all the local football in the Observer, out on Thursday