Lee Holmes put improving North End ahead, slotting Stuart Beavon's pass under Eirik Holmen Johansen, before Nicky Wroe pounced on the on-loan keeper's poor clearance to make it 2-0.
King rifled against the post late on but nodded in Jeffrey Monakana's cross soon afterwards to seal the win.
The defeat left the Iron in the bottom four zone on goal difference.
Scunthorpe are level on points with Oldham but the Latics have two games in hand.