The dropped points meant that Bognor surrendered their lead at the top to Dulwich who now lead by two points.
The Rocks management made one change to the starting line-up from their previous match. Fit-again Ben Andrews came in for Harvey Whyte, who dropped to the bench.
In the opening few seconds there was a scare for the Rocks when Luke Blewden appeared to be upended just inside the box, but referee Mr Pike waved away all protests from the home players.
In the seventh minute, Bognor’s first chance came through Terry Dodd, who chased a ball played over the top. But he dragged his effort wide from 20 yards.
The Rocks, however, were in front in the 14th minute when tricky play on the left from Johnson saw his cross find Dodd, who headed home from six yards.
The Rocks were asking all the questions and soon afterwards home keeper Zawadski dropped Kane Wills’ corner. The ball fell into the path of Stuart Axten who saw his effort blocked.
But on 20 minutes the Rocks doubled their lead through a fine individual effort from Johnson, who curled his effort home from the edge of the box.
Just before the break, Dodd chased a ball on the right before finding James Crane who sent his curling effort just over the bar.
Ten minutes into the second half, the hosts pulled one back in controversial circumstances.
A long ball was pumped forward by Anthony Storey and Blewden appeared to shove Axten before lobbing the ball over the stranded Craig Stoner in the Rocks goal.
Back came Bognor and on the hour mark substitute Antonio Gonnella, on for Jon Marzetti, fed Dodd whose shot on the turn was deflected wide.
From the resultant corner, Osa Obamwonyi struck the ball goalwards from 20 yards but Zawadski was equal to it.
In the 71st minute, the hosts levelled when the Rocks failed to clear their lines and Tom Burton was on hand to poke home from close range.
Crawley Down then completed their incredible turnaround ten minutes from time when Fraser Logan received the ball 20 yards out before cutting inside and unleashing an unstoppable low drive past Stoner.
The Rocks and their travelling fans couldn’t believe it, but they rescued a point two minutes into stoppage time when the ball ricocheted kindly for Johnson to fire home from 12 yards.
The title is still in their own hands - but Dulwich look strong and Jamie Howell and Darin Killpartrick’s can afford no more slip-ups.