Yeovil had themselves looked poised to get a late winner but Palace broke quickly and substitute Kieron Djilali got in a cross from the left and Lee beat the defence to shoot into the roof of the net.
Darren Ambrose, Nathaniel Pinney and Lee all had good chances in the first 10 minutes, Pinney's being the pick of the efforts as his 18-yard effort forced John Sullivan to tip over the bar.
The Championship side had a let-off when Luke Freeman, on loan from Arsenal, hit the bar as Yeovil responded to a spell of Palace pressure.
Dean Bowditch had two chances for Yeovil as the half wore on before a fallow period ensued before and after the break.
George Burley rang the changes but it took a while for them to take effect, only for Lee to pounce late on and spare his side's blushes.