Rak-Sakyi headed Palace in front just after the half-hour mark and then five minutes later, he grabbed his second with an excellent finish.
Josh Shonibare pulled one back for Derby on the hour-mark.
With 15 minutes remaining, Rak-Sakyi secured his hat-trick from the penalty spot.
The south Lononders eventually saw out the remaining 15 minutes of normal time, and a protracted eight minutes of stoppage time, to confirm their fifth place finish in their first ever Premier League 2 Division 1.
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