Whitaker wrapped up the points with the second goal in the space of three minutes after Craig Davies had broken the deadlock on the hour mark. It means John Sheridan's men stay two points clear at the top of the table ahead of Port Vale.
Chesterfield looked strong early on as Jack Lester released strike partner Davies in the 17th minute but he dragged wide when well placed.
Drew Talbot was a constant threat for the Spireites and his right-wing deliveries looked the most likely way the deadlock would be broken.
The game caught fire in the second half - former Spireite Wade Small had Aldershot's best chance, dragging wide when clean through on goal
Chesterfield always looked dangerous and on the hour in-form Davies cut inside onto his right foot and bent a stunning strike into the far corner, his 12th league goal of the season. Aldershot were shell-shocked and three minutes later Whitaker coolly slotted into he far corner for his ninth of the season from Lester's lay-off.