Two quick goals from Mile Jedinak and Damien Delany looked to have put Palace in control before Millwall pulled one back through Liam Trotter's penalty after Dean Moxey had been sent off for handball.
Henderson in particular should have given his side the lead, but he could only head wide.
However, they did finally make the breakthrough on 35 minutes when Jedinak fired in from distance.
It got better for Palace moments later as Delaney rose to nod home Owen Garvan's cross.
However, Millwall cut the deficit minutes before the half-time whistle through Trotter's penalty after Moxey had received a red card for clearing the ball from under the crossbar with his hand.
The visitors nearly snatched an equaliser in first-half injury time, but Chris Taylor's effort could only rattle the crossbar.