Andrew Hughes, Joe Rafferty, Sean Maguire and Emil Riis scored the goals which sent PNE through on Tuesday night.
The draw for the last 16 will be made on Wednesday evening live on Sky Sports.
Here are the PNE player ratings from the game, with several strong performances.
1. Declan Rudd 7
Not overly troubled during the game, had no chance with Vassell's goal. Kicking and handling was good. A late booking for dissent. Photo: Dave Howarth/Camerasport
2. Jordan Storey 7
Started on the right of the back three and moved into the middle when Liam Lindsay went off. Had more to do when Vassell joined the action in the second half. Photo: Dave Howarth/Camerasport
3. Liam Lindsay 6
The centre-half saw his night end after half an hour because of a knee injury. Had been fine until then. Photo: Dave Howarth/Camerasport
4. Andrew Hughes 8
Excellent performance from the Welshman, defended well, good use of the ball from the back and scored the first goal with a powerful header. Photo: Dave Howarth/Camerasport