Palace were also denied by Millwall goalkeeper DavidForde, who managed to scoop the loose ball clear from Darren Ambrose's free-kick clear, with Pablo Counago ready to pounce.
Burke, only recalled because of injury to Michael Chopra, had danced around the covering defenders before poking a miss-hit effort through a crowd of bodies and it trickled into the corner of Millwall stopper David Forde's net.
As PSG continued to dominate, David Hellebuyck had Forde scrambling back to push away a long-range effort in the 33rd minute and Darren Kelly then did brilliantly to clear Albert Baning's shot off the line.