It was only their second home league win of the season - the other having come with an identical scoreline against East Thurrock in August.
The Rocks welcomed back Dan Beck to the bench while Kane Wills returned to the starting line-up after a three-match suspension. Ashley-Paul Robinson and Steve Harper both started in a stronger-looking line-up.
Louis John had to belt clear a cross as Thurrock threatened down the left - then Richie Jones’ cross come shot flew narrowly over.
Luke Wandis crossed from the right to Charlie Stimson, who volleyed well over the bar.
Harvey Whyte tried to thread in Crane on the run but Wandis tracked back and shepherded the ball to safety.
Harper went to ground under pressure from Matt Turpin after a cross from Jon Marzetti.
Whyte beat right back Jones for pace before curling a cross in. Turpin headed clear.
Good work from Robinson deep in the Thurrock half led to Lewis Stockford having a shot blocked. Robinson’s follow-up was smashed high and wide.
Stockford sped into the box to have the hosts’ first attempt on goal and forced David Hughes into a fine low block down to his left.
Whyte received a yellow card for fouling Jones near the corner flag.
Ben Walster had to produce a fantastic sliding tackle to deny Whyte on the run. The resultant corner from Wills fell to Matt Partridge and was pushed away by Hughes.
On 30 minutes Crane teed up Whyte down then left and his shot was blocked by a defender.
Ben Smith slid a shot wide of the post on the turn after a pass from Stimson.
A lay-off from Crane found Harper just outside the box, but his low shot was deflected into Hughes’ arms.
A neat turn from Robinson allowed him to set up Harper, who made no mistake in slotting in - only to have it scrubbed out for offside.
Bognor went ahead on 45 minutes when Crane (pictured above by Tommy McMillan) followed up a Whyte pass to slam home a low shot.
Robinson let fly with a shot from well outside the box but it flew wide of the post as the rain poured down at Nyewood Lane.
Crane had a chance to score inside the box after beating his marker. His low shot was blocked by the legs of the keeper.
Harper’s low cross found Robinson in the box but somehow the striker’s shot from close range was blocked and Hughes gathered on the rebound.
Thurgood’s inswinging free-kick bounced high inside the box but evaded all of his fellow players as Bognor were allowed to clear the danger.
Wandis was replaced by Callam Ibe and Harry Honesty came off for Leroy Griffiths on 57 minutes for the visitors.
The 68th minute saw the triumphant return of Beck, who replaced Daryl Wollers to a great reception from the majority of the 444 crowd.
Wills set up Stockford, who was sprinting on to the ball. The midfielder’s cross was too far for Robinson or Harper.
On 72 minutes Mu Maan came on for Stockford.
Robinson won a free-kick after he was brought down by Jack Jeffries. Robinson hit the free-kick straight into the wall.
Robinson went to ground under a stiff challenge from Ben Walster and had to be replaced by Carl Walshe on 82 minutes. Walster received a yellow card for the foul.
Whyte was spoken to by the referee after he slid in late on a slippery surface into Hughes as the goalkeeper gathered. With Whyte already on a yellow card, the referee decided to warn him.
Maan’s left-footed attempt from long distance failed to trouble the goalkeeper, as it swung over the bar.
Thurgood’s free-kick into the box found Smith but his header went wide of the right post.
Craig Stoner had to gather to ensure Thurrock didn’t score late on as Crane tracked back to defend.
The Rocks were glad to hear the final whistle immediately after their close shave.
Rocks: Stoner, Marzetti, Wollers, Crane, Partridge, Whyte, Wills, Harper, Robinson, Stockford. Subs: Beck, Maan, Tuck, Walshe, Boyle.
The Rocks host Havant & Waterlooville next Saturday in the third qualifying round of the FA Trophy.