Despite lagging well behind in the possession stakes at half-time (28%-72%), the hosts led 2-0 at the break thanks to a double from the returning Ronan Curtis.
Pompey were then quick to add to their lead in the second half, with Tom Naylor and John Marquis both finding the back of the net before the hour mark.
Oliver Finney scored a late penalty to deny the hosts a clean sheet but the margin of victory still sees Kenny Jackett’s men move up to fourth in the table.
The wins sees the Blues move up to third in the table – three points behind leaders Hull.
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9. Ronan Curtis - 8
Good performance following a tiring week while away on international duty. Set Pompey on the road to victory. Photo: JPIMedia
10. John Marquis - 7
On the scoresheet again, albeit in fortunate fashion. Photo: JPIMedia
11. Ellis Harrison - 7
(replaced by Jordy Hiwula on 86 minutes): Didn't get on the score sheet, but holds up play so well. Photo: JPIMedia
12. Callum Johnson - 7
(replaced Haji Mnoga on 46 minutes): Steadied things down on the right. Photo: JPIMedia