Wright-Phillips set Charlton on their way to a record-equalling club record of away victories just before half-time and struck twice more either side of a Johnnie Jackson finish to give Charlton a 12th league win on the road this season.
Charlton always looked to have the edge and it needed a great save by Tommy Lee to keep out a Yann Kermorgant header in the 19th minute.
But Lee was beaten by a deflected cross from Danny Green that came off the inside of a post in the 43rd minute and Wright-Phillips turned the ball over the line.
The floodgates opened after the break as Wright-Phillips hooked in a shot in the 57th minute with defenders looking in vain for an offside flag and a minute later Jackson sidefooted in from eight yards with Green again the provider.
Chesterfield were pulled apart in the 67th minute when Green crossed low and Wright-Phillips steered the ball inside the left post to put Charlton a step closer to the Championship.