Reeco Hackett, George Hirst, Aiden O’Brien and Sean Raggett did the business with a much-improved showing from Danny Cowley’s men after the break, following an awful first half in front of a crowd of 14,767.
The opening 45 minutes was low on quality, but the tempo was ncreased after the interval, as the Blues picked up back-to-back league wins for the first time since November.
It was a poor first half which required Sean Raggett’s goal-line clearance to stop Pompey going in behind at the interval.
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That happened in the 27th minute, with the only incident of note beforehand being Reo Griffith’s 20-yarder being saved by Gavin Bazunu at the second attempt.
Pompey mustered a couple of half chances from George Hirst and Michael Jacobs, but there was little for the Fratton faithful to get excited about.
There was a huge missed opportunity to open the scoring two minutes after the restart, as George Hirst completely missed Hackett’s cross from close range.
Hackett woke Pompey fans from their slumber after 56 minutes as he opened the scoring with a powerful back-post
And the Blues were in control seven minutes later, as Ben Jackson gifted the ball to Hirst who advanced and fired past Jonathan Mitchell despite a heavy first touch.
O’Brien put the gloss on a dominant second half for Pompey with nine minutes left, as he bundled home Curtis cross from close range.
And there was still time for man of the match Sean Raggett to head home Hackett's free-kick in stoppage time.