The Rocks had to settle for a point from an entertaining clash with Oxford City at Nyewood Lane.
They were the better team for long periods but couldn't find a goal - and were almost made to pay when City had two gilt-edged chances to nick it late on, both thwarted by superb Dan Lincoln saves.
A point was not enough to move the Rocks out of the bottom three but it does give them four points from two games, which is a big step in the right direction.
Bognor were without two of those who started Saturday's win at St Albans - midfielder Doug Tuck through illness and forward Connor Tighe, whose loan from Whitehawk has ended.
Harvey Whyte and Ollie Pearce came into the starting line-up in their places.
Oxford's team included former Rocks defender Joe Oastler, ex-Rocks target Matt Paterson and Christian Oxlade-Chamberlain, on loan from Pompey.
It was a critical game at the bottom of the table - Oxford sat one point and one place above their hosts in the relegation zone at the start of play, with both sides knowing a win would take them out of the drop zone. For Oxford a point would do that at Poole's expense.
The Rocks won a free-kick on the angle of the penalty area in the fourth minute when Kristian Campbell's mazy run was halted. Pearce's attempt was blocked by the wall. Then Ben Swallow swung in a lovely cross from the left but keeper Jack Stevens got there first.
Calvin Davies put Pearce through on goal with a neat pass down the right but the offside flag went up. Soon Pearce whacked a dangerous low ball across the box that was cleared to Davies, whose fierce drive deflected off Swallow's boot and out for a goal-kick.
There was a let-off for Bognor on 16 minutes when the ball was pulled back to the unmarked Paterson 15 yards out and he had time to place a low shot towards the bottom corner. It beat Lincoln but came back off the post.
Whyte got his head on the end of a Beck cross from the left on 22 minutes but it was too high. Davies' long ball fell perfectly for Pearce in the area but after taking a touch, his goal-bound shot was blocked.
Oxford had a couple of dangerous moments but for the most part the Bognor defence coped quite comfortably with what they had to offer.
Ibra Sekajja brought the crowd to life with a lovely bit of close control and a run that took him past three players, but his shot was blocked.
Oxford brought on Reece Fleet for Dave Pearce at the start of the second half.
The Rocks were doing many things right but another fine cross by Swallow - this one from the right - couldn't find the head of Sekajja or Davies, who had ventured forward.
Sekajja tried a 30-yarder and struck it well but straight at Stevens. Davies did the same from almost as far out but it was just as comfortable a take for the keeper. And it was three shots in four minutes as Sekajja tried one with his left foot but it was wide.
Oxlade-Chamberlain threatened down the City right but after bursting into the box he blazed his shot - or was it a cross - out of the ground.
Oxford made their second change on 63 minutes with Horatio Hirst replaced by Ezra Forde. The Rocks made a change of their own, Beck making way for Joe Lea.
A great chance for a Rocks lead came and went on 67 minutes as Pearce and Sekajja led a quick break but the latter's ball across the box was too far in front of his forward partner. The follow-up attack ended with a Campbell shot that was wildly high.
The Rocks' pressure was growing and Sekajja squared for Lee but his sidefooted attempt was bravely blocked by a leaping defender.
Oxford were still having their moments although one attack ended in a woeful finish from Godfrey Poku.
Paterson looked certain to score with 16 minutes left when the ball was squared to him ten yards from goal but a defender was quick to close him down and charge down the shot.
Jimmy Muitt came off the bench on 76 minutes in place of Pearce.
Lincoln was almost caught out as the game entered the final ten minutes when he came out to gather a through-ball but didn't get there first - but Sami El-Abd got him out of trouble.
Whyte headed over from a Muitt cross - then Lincoln saved the Rocks conceding with just four minutes left, getting down to palm away a Zac McEachran shot after the ball was gifted to Oxford. Lincoln and El-Abd had to be separated as they argued fiercely after the incident.
Lincoln came to Bognor's rescue again a minute later by leaping to push a deflected Forde shot over the bar. These were nervy, nervy moments for a home team still short on confidence.
In stoppage time Swallow did superbly to keep a long pass by Field in play by the corner flag and when he sent over a cross to the far post, it was just too high for Muitt whose header went over.
That was the final chance and when the whistle blew, both sides must have felt the same - slighty aggrieved they had not won but glad at least they had not ended pointless.
The Rocks now turn their attentions to the FA Trophy - they visit Hemel Hempstead on Saturday - but another big league game looms on Saturday, December 2, when Concord Rangers visit the Lane.
Rocks: Lincoln, Davies, Campbell, Beck, El-Abd, Field, Whyte, Block, Sekajja, Pearce, Swallow. Subs: Muitt, Lea, Scutt, Boughton.
Oxford C: Stevens, Oxlade-Chamberlain, Grant, Fofana, Navarro, Oastler, Hirst, Poku, Paterson, McEachran, Pearce. Subs: Jones, Forde, Fleet, Tutton.
Ref: Jacob Miles (Peacehaven)
Att - 501