Paul Gallagher opened the scoring on the stroke of half time before Callum Robinson scored against his former side to double their advantage.
Cauley Woodrow got a goal back for the Robins but it was too little too late, coming in the final minute of the game.
The win extended PNE’s unbeaten run against City to nine games, eventually extending the run to 15 before a loss in Janaury last year.
PNE Starting XI: Maxwell, Fisher, Davies, Huntington, Woods, Barkhuizen, Johnson (Robinson, 61’), Pearson, Gallagher, Hugill (Clarke, 90’), Mavididi (Browne, 56’).
PNE subs not used: Rudd, O'Connor, Harrop, Welsh.