Notts, who have now lost seven of their last eight matches and are only 12 points off the League Two relegation zone, looked comfortable until Bennett shot home just before the break.
Bennett made it 2-0 when he slotted in just after the restart.
A Christian Burgess header and Marc McNulty's lob sealed a win which keeps Pompey five points off the top three.
Kyle Bennett scored twice as Portsmouth thrashed Notts County in Mark Cooper's first game in charge of the Magpies.