Pitman got the Cherries off to a perfect start in the 12th minute when his shot ricocheted off the foot of visiting defender Rory McArdle and looped into the far corner.
Liam Feeney, signed in early February from non-League Salisbury City, then doubled Bournemouth's lead midway through the first half.
He cut in from the right and sent a rasping left-foot shot into the top corner.
Pitman made it 3-0 in the 67th minute, seizing on a neat flicked header by Steve Fletcher to drill a sweet left-footed shot into the bottom corner.
He completed his treble in injury time with another crisply-struck shot into the far corner.