Bournemouth moved up to fifth position in npower League One as a result of a comfortable victory, while Crewe stay in mid-table.
Pitman's opening goal came in the eighth minute with his first penalty coming after Marc Pugh had been brought down by Adam Dugdale.
Crewe went further behind in the 67th minute when Pitman scored from close range after being set up for an easy finish by Josh McQuoid.
The visitors pulled a goal back in the 76th minute when Ryan Colclough, who had come on as a substitute 13 minutes earlier, turned in a centre from Mattias Pogba for his first senior goal.
But Pitman made sure of Bournemouth's points with a penalty eight minutes from the end to complete his first hat-trick since August 2010.
Abdul Osman fouled substitute Wes Fogden and Pitman again made no mistake with the spot kick.
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