Burgess Hill got off to great start with a bursting run down the left by Marcel Powell. He pulled the ball back to Finney, who did well to net it low beyond a diving Ryan Hall.
Bognor were struggling to get hold of the ball as Hill’s Reggie Ward sped down the right but he ran the ball out of play. A long ball forward towards Jasper Mather saw him try to track it down but it ran out of play.
Bognor won a free-kick just outside the box as Mather was fouled. Calvin Davies hit the ball swirling through the wall but ex-Rock Taylor Seymour, in goal for Hill, pushed it back out of the area on 20 minutes.
Kieran Rowe hit a ball in high into the area but Hall was fouled. Davies gave away a free-kick and Kieron Pamment curled it into the area but Finney, sliding in, couldn't quite get to it.
Mather found Rabbetts on the left and the he hit it fiercely across goal and it was Seymour who steered it around the frame of goal. Before the corner, Darren Budd went into the book after arguing with the referee. Isaac Olaniyan miscued the ball completely following the corner kick and Davies was blocked with his strike.
Olaniyan was denied with his low cross but was blocked from the left flank. On 38 minutes it was a good turn in midfield by Matt Burgess which saw him find Rabbetts on the left. He swung in a cross but there was no team-mate up with him to capitalise.
Davies' corner was headed out at the near post and Olaniyan's cross towards the back post was just out of the reach of Douglas on 42 minutes.
Another neat turn by Burgess saw Bognor spring on the attack. He passed to De St Croix, who got to it before winning a corner. Davies did well to find Douglas in the area but he headed it well wide, ending a frustrating first half for the visitors. HT 1-0
Early in the second half De St Croix won a corner on the right. Davies crossed it but Douglas glanced his header wide. A quick clearance saw Bognor win possession but De St Croix's forward pass towards Tommy-Lee Higgs was cut out.
Powell was making some good runs as he beat Douglas down the left but the ball had rolled out of play. The Rocks went close as Olaniyan had a 22-yard strike destined for the top left corner denied by a decent diving save by Seymour. Then De St Croix, on the rebound, fired it over the bar on 52 minutes.
Harvey Whyte came on for De St Croix on 53 minutes. On 56 minutes Higgs capitalised on a swift Bognor attack and hit one with his left foot on the rise and the ball cannoned off the post and away. Dan Smith came on for Higgs on 59 minutes.
Another free-kick from the left by Davies saw him hit it into the area but Douglas couldn't reach it in the air. Down the other end, Martyn Box's run down the left ended with the full-back crossing it. The ball fell to Powell, who diverted it high over the bar on the bounce.
Powell had beaten Douglas for pace and had only Hall to beat but the goalkeeper denied him. Rob O'Toole crashed the ball off the crossbar from yards out after a deflection off Ben Anderson on 68 minutes.
On 65 minutes Bradley Lethbridge replaced Olaniyan on the left in Bognor's last change. There was a period where Rocks were down to 10 men after Douglas had to receive treatment which added to the pressure they were under.
Rowe hit another chance over the bar for the Hillians as Rocks were struggling to create much. Frustrations grew as another cross from the left by Rabbetts sailed through the area with no Bognor player alert to the chance.
Douglas committed a foul on the left on 77 minutes. Box curled the free-kick in but Jack Taylor diverted his header over the bar.
Lethbridge won a corner on the left for Bognor. Smith headed the ball across goal following a cross and Craig Robson shot at goal but was deemed to have handled the ball.
Lethbridge did well to speed down the left before diverting the ball across the box to Mather but right in front of goal he was denied straight away by Seymour.
Bognor committed another foul just outside the box. Left-back Box was the free-kick taker but his strike sailed straight to Hall who caught it confidently.
Rabbetts did so well to track down a long diagonal pass. He passed it inside and it was Davies who diverted it further inside the box but Mather couldn't gettot it and then Anderson scuffed his strike well wide of the goal on the follow up.
Smith missed a couple of half-chances and Davies whipped in a corner that was cleared.
Burgess Hill went down the other end and scored their second. Box did well to run down the left before putting the ball on a plate for Finney to nod it down and into the net deep into stoppage time.
Next up for the Rocks is a trip to Enfield on Saturday.
Rocks: Hall, Anderson, Rabbetts, Davies (c), Douglas, Robson, De St Croix (Whyte 59), Burgess, Higgs (Smith 59), Mather, Olaniyan (Lethbridge 65)
Subs not Used: Howick, Ogundega, Briffa, Jammeh