Nathan Odokonyero scored twice and James Crane saved a point with an 88th-minute goal as the Rocks refused to be beaten in north London.
Kayne Diedrick-Roberts was in the starting XI while Harrison Brook dropped to the bench at a chilly Coles Park. Bognor fielded just four substitutes as Joe Cook was still recovering from injury and Gavin McCallum is scheduled to return in the New Year.
Bognor started brightly as Harvey Whyte received the ball from a pinpoint Ashton Leigh cross. The ball fell on to Whyte's right boot but it rebounded off a defender and off him as it rolled out for a goal kick.
Jordy Mongoy passed to Jake Flannigan on the right but he was blocked. Flannigan had another cross cut out as Lamar Joseph-Johnson caught his looping ball into the box. Then Georgios Aresti spotted Amadou Tangara off his line and chipped a curling strike from the edge of the box. The Bognor goalkeeper had to tip the ball over his crossbar.
Whyte played a hopeful ball towards Odokonyero which was cut out by the defender but Leigh pounced on the loose ball before hitting a chance along the deck that was comfortably saved.
Alfred Bawling beat the offside trap on the counter. He rounded his man before running along the byline before shooting from a tight angle and forcing a parried save from Tangara for a corner. Rakim Richards couldn't put away a chance from the cornner.
Craig Robson diverted a corner wide of the post with his right leg. Tangara had to rush out of his goal to head the ball out on the edge of his box.
Ethan Robb made a mistake, letting Bawling through on goal after losing possession easily. Bawling punished the Rocks and confidently dispatched it high into the top corner beyond a diving Tangara on 25 minutes. Bognor got the equaliser on 32 minutes. Robb had a shot on goal which bounced awkwardly in front of the goalkeeper. Mongoy tried to scramble it in and Odokonyero smashed it high into the roof of the net.
Bawling teed up Andronicos Georgiou who prodded the ball square to Georgios Aresti - but he bounced his fierce attempt wide of the post. Flannigan’s ball in was headed out by a Haringey defender before Diedrick-Roberts pounced to hit it on the volley and agonisingly wide of the post from the edge of the box in the 45th minute. A late first half corner was awarded to the hosts but Michael O'Donoghue's corner kick was well gathered by Tangara. HT 1-1
Davies picked out a great run from Diedrick-Roberts who sped inside before curling a shot well wide from a tight angle. Georgiou hit a chance from outside the box that Tangara gathered at the second attempt. Diedrick-Roberts went down under a challenge and had to receive treatment from Bognor’s physio.
Adeyinka Cole cut inside before curling it high at goal in Haringey's first attack of the half. Tangara tipped it over the bar with one hand. Scott Mitchell hooked a loose ball over his head straight at Tangara.
Georgiou made Bognor pay for their missed chances. His shot was only partially pushed up by a diving Tangara, who failed to get back to his feet in time as an onrushing Bawling headed in from close range on the rebound on 58 minutes.
Charlie Bell replaced Leigh on 64 minutes for Bognor before Mitchell went into the book for the hosts as Bell was fouled. Davies hit the free-kick straight into the wall. Bawling was fouled and Robb went into the book. Diedrick-Roberts was replaced by Yasseir Nazor on 71 minutes.
Rocks got their second equaliser on 72 minutes. Mongoy's long range effort was pushed on to the crossbar and spun up into the air and Odokonyero knocked it in at the back post. But the scores weren't level for long. A cross went across the Bognor penalty area and the ball was cut back by Aresti for Jorge Djassi-Sambu to divert the ball low into the net on 74 minutes.
Cole got a yellow card for a late sliding challenge on Nazor. Sami Bessadi replaced the booked Cole for the hosts.
Harrison Brook came on for the remaining minutes for Mongoy on 86 minutes. And Bognor found their third equaliser right at the end. Bawling deflected the ball out seemingly from a throw-in. But the referee instead awarded a free-kick. Davies's kick was brilliantly placed and the ball curled right on to the head of an unmarked Crane, who powered it in on 88 minutes.
Nazor was fouled running in from the wing. Davies dipped a cross in from the free-kick and with Whyte in pursuit it was nodded out over the bar by a defender, but a corner was not awarded to Bognor.
* Bognor welcome Corinthian Casuals to Nyewood Lane on Tuesday (7.45pm).
Rocks: Tangara, Flannigan, Crane, Davies, Robb, Robson, Whyte (c), Diedrick-Roberts (Nazor 71), Odokonyero, Leigh (Bell 64), Mongoy (Brook 86). Subs not used: Dandy.