Bognor made it four points from their first two National League South games as Corey Heath and Jimmy Muitt struck in a game that could have gone either way.
The 2-2 draw leaves Bognor sixth after a pleasing first few days of the campaign.
The starting XI was unchanged from the one that saw off Bath 3-2 though Pat Suraci returned on the bench.
Poole's Corby Moore swung a ball in to Tony Lee but he was closed down. Then Steve Devlin struck one on the volley that was blocked by Sami El-Abd's chest.
Devlin received a yellow card after only seven minutes as he tugged Ben Swallow to the floor. Ollie Pearce, matchwinner from a dead ball on Saturday, put the free-kick wide. Alex Parsons won the ball deep in the Dolphins half and Muitt's cross had to be hastily cleared by Jake Smeeton.
Bognor went ahead on eight minutes. Pearce's corner found an unmarked Heath, who ran in to power a header in beyond the goalkeeper.
Devlin cut inside before letting fly with a left-footed effort but skied his chance over the bar on 15 minutes. Doug Tuck found Parsons, whose cross was cleared by Moore. Shaun Cooper levelled for the hosts on 24 minutes after good work by Devlin on the right. Cooper struck it with his left boot and it dipped into the bottom corner beyond the diving Dan Lincoln.
Another Pearce corner found Heath on 28 minutes but his header went wide. Another corner by Pearce was pushed away by Nick Hutchings. Moore required treatment which held up play for a couple of minutes on the half hour. He did return to the field later all bandaged up.
Luke Burbidge beat Heath before shooting low. Lincoln did well to deflect it away with his leg on 36 minutes. Some great work saw Swallow tee up Pearce and his ball along the line picked out Calvin Davies, who beat his man before crossing. But the Dolphins cleared the danger.
Heath was tripped near the corner flag. Swallow's free-kick was headed out to Tuck, who struck it on the volley, forcing Hutchings to push it over the bar. Muitt's cross had to headed out by Moore, then Parsons' chipped cross was gathered by the goalkeeper. Swallow tried his luck from long distance but he skied his effort inside the two minutes of stoppage time.
From kick off, the Rocks were asleep and Lee capitalised by curling a shot over Lincoln and into the net from 25 yards to put Poole 2-1 up.
Muitt set up Swallow for a shot that was high and wide. Dan Beck struck an attempt wide after good build up by Tuck, Pearce and Davies. El-Abd cut out a forward pass and then Parsons spun his marker neatly before shooting rather weakly along the deck.
Pearce used his pace to beat his marker but his cross flew off for a goal-kick. Abdouli Baggie used his trickery to get down the left before crossing but it was headed it out for a corner. Swallow swung in a neat dipping cross from the right and found Parsons, who guided it towards goal only to bring a fabulous diving save by Hutchings on 61 minutes.
Jack Dickson smashed a shot over the bar with the outside of his boot. Pompey academy player Christian Oxlade-Chamberlain - brother of Alex - replaced Lee on 65 minutes for the hosts.
Parsons was booked for a sliding challenge on Will Spetch before Harvey Whyte was tripped inside Poole's half and Cooper was booked. Joe Lea replaced Parsons on 69 minutes meaning Rocks changed to 4-4-2, with Muitt and Pearce leading the front line.
Jez Bedford, another Pompey youngster, replaced Baggie on 75 minutes for the hosts. Swallow and Davies were causing havoc on either side before the ball fell to Beck who smashed it low but wide of the left post on 81 minutes.
A wonderful turn by Lea saw the Rocks on the attack. He passed forward to Muitt in space and he turned and shot straight into the bottom left corner on 84 minutes to the delight of the many Rocks fans in attendance, levelling it up at 2-2
Pearce came off for Jimmy Wild on 88 minutes. Poole were briefly down to ten men as a player was injured. Burbidge hit one but Lincoln saved comfortably. Muitt sensed glory and curled one at goal but Hutchings fisted the ball away.
Late on Rocks won a corner on the right. Swallow swung it in but Poole dealt with it.
Bognor continue on their travels this Saturday when they visit Welling.
Rocks: Lincoln, Whyte, Davies, Tuck, El-Abd, Heath, Muitt, Beck (c), Parsons (Lea 69), Pearce (Wild 88), Swallow. Subs Not Used: Charman, Block, Suraci
Attendance - 487