Lions boss Kenny Jackett has yet to decide whether to make Puncheon's loan deal from Southampton a permanent transfer this month, but the winger is certainly putting forward a strong case.
He stunned Palace with an early opener and then struck twice more in the second half to leave Millwall on the coat tails of the play-off pack.
The Eagles, by contrast, remain rooted in the bottom three after their winless run stretched to five matches.
Millwall got 2011 off to a perfect start with a goal after just eight minutes, Puncheon rifling the ball home from just inside the box after Palace failed to clear Josh McQuoid's header.
He grabbed his second in the 64th minute from Scott Barron's pass and completed his treble six minutes later from Liam Trotter's cross.