The Cherries went ahead when Marc Pugh crossed from the left and Matt Tubbs's header back across goal was met on the volley by Brett Pitman, who found the net for the fifth successive game.
Iron keeper Eirik Johansen saved well from Harry Arter and Eunan O'Kane, while Pitman rattled the crossbar.
Mark Duffy had Scunthorpe's best chance but dragged his shot wide.
Eddie Howe's side are now three points clear of third-placed Brentford, who lost 2-0 at Milton Keynes but have two games in hand on the Cherries, while Scunthorpe drop into the bottom four after rivals Oldham drew with Colchester.