Pitman broke his duck with his first league goal for the Robins in the defeat of Leicester last weekend and he added two more to his account with spot-kicks after six and 34 minutes.
Keith Millen's side were given the opportunity to take an early lead when Leon Britton brought down David Clarkson. Pitman seized the chance with a superbly-placed penalty into the top corner.
Albert Adomah threatened in the 30th minute before a handball by Stephen Jordan enabled City to extend their lead, Pitman again obliging from the spot.
United's day got worse when Richard Cresswell was sent off moments before half-time after he went charging in on Marvin Elliott.
Their misery was compounded just after the hour mark when Jamie McAllister's corner flew straight over goalkeeper Steve Simonsen and into the net.
Source: PA
Source: PA