Pitman took his tally to 15 since rejoining Bournemouth from Bristol City in November with an 11th-minute goal.
Marc Pugh centred from the left and Matt Tubbs provided the opening for Pitman to volley home.
Pitman also hit the bar in the second half while Bournemouth were denied further goals by Norwegian goalkeeper Eirik Johansen.
Johansen, on loan from Manchester City, kept out efforts from Harry Arter, Matt Ritchie and Eunan O’Kane.
Scunthorpe’s best chance fell to striker Mark Duffy in the 54th minute but he dragged his shot wide from 15 yards with the goal at his mercy.