Burley was responsible for bringing the former Tottenham striker to Selhurst Park but he was sacked following the 3-0 defeat to local rivals Millwall on New Year's Day, which was the final straw for Palace, who had slipped to second from bottom in the Championship under the Scot's charge.
Former fans' favourite Dougie Freedman was left to take charge against fellow strugglers Preston on Monday and he was given an ideal start in the battle of the managerless clubs.
Following a tepid first half in which chances were at a premium, Iversen - who completed his free transfer from Rosenburg on Sunday and was only allowed to play after being given international clearance earlier on today - wasted no time in making his mark.
The 34-year-old headed home from Kieron Cadogan's right-wing cross just before the hour mark to give Palace their first win since November.
Iversen's strike deepened Preston's woes, who now find themselves firmly rooted to the bottom of the Championship and seven points shy of safety.
Freedman, who took charge of the Eagles on Sunday, wasted no time in stamping his authority on the team as he made five changes to the side that suffered the humiliating defeat to Millwall.
Preston's caretaker boss David Unsworth, whose first game in charge was their 2-1 loss to Derby on New year's Day, made four changes to his side.
North End are another club who are in dire straits and just one win in 10 has seen them slump to the foot of the league table.
Given both teams' standing, it came as no surprise that the game started rather tentatively, with the best chance falling to Neil Danns, whose drilled shot was easily saved by Lilywhites goalkeeper Andy Lonergan.
The two sides played out a 4-3 thriller in the reverse fixture in October but defences were well and truly on top in the first half in London, although had Andy Dorman managed to get anything on Wilfried Zaha's cross, he surely would have put the hosts in front.
At the other end, Paul Hayes swivelled and volleyed wide after the ball had been allowed to bounce in the Palace area.
Palace made a bright start to the second half and Dorman should have done better when he cut into the box from the left and skied his effort.
Preston then thought they should have been awarded a penalty when Keith Treacy was felled following a challenge from Paddy McCarthy, however, the midfielder was given a yellow card for a dive.
The visitors would have felt even more aggrieved when Iversen headed Palace in front after 58 minutes.
Cadogan's right-wing cross found Iversen at the back post and he leapt highest to nod the ball past Lonergan.
Barry Nicholson spurned a golden chance to equalise when he headed wide from Billy Jones' cross, while Cadogan missed the chance to seal the victory when he struck wide when clean through on goal.
It did not matter however and Palace were able to claim their fifth successive victory over Preston at Selhurst Park.