Gareth Evans put Paul Cook's side ahead from the spot after a foul on Kai Naismith by Richard Duffy.
The Magpies drew level in the second half, however, when Jorge Grant found the corner from Elliott Hewitt's pass.
Jamal Lowe restored Pompey's lead with an angled shot in the second half and made sure of victory - and eventual promotion - with a second in the 90th minute.
The official Notts site has published the game highlights - see how the game panned out for yourself.
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