Kyle Bennett struck either side of the interval, with a couple of goals that were extremely easy on the eye.
Christian Burgess then opened his account for the club before Marc McNulty came off the bench to add an extra gloss to the scoreline.
Paul Cook made four changes from the side that drew at Mansfield the previous week.
Paul Jones was recalled from his Crawley loan to replace Ryan Fulton – who had been called up to the Scotland under-21 side – between the sticks.
There were also starts for Gary Roberts, Adam McGurk and Matt Clarke, with McNulty, Kal Naismith and Adam Webster dropping to the bench.
Before kick-off there was a minute’s silence in memory of former Pompey left-back Jack Mansell – who passed away last week – and the victims of the attacks in Brussels.
When the game got underway, the hosts made a bright start to match the fine conditions on the south coast.
And Michael Bull earned the ire of the Fratton faithful for not awarding their side a penalty after just a three minutes.
It looked a clear foul from Haydn Hollis on Ben Davies as the right-back charged into the box, but the referee was not convinced.
However, the first half was ultimately a scrappy affair, with plenty of fouls interrupting the flow of the game.
Stanley Aborah collected the first booking for a late challenge on Michael Smith, not that it stopped the midfielder from getting involved in a few more dubious challenges.
There were not too many shots to trouble either of the goalkeepers, with Curtis Thompson seeing his dangerous run eventually halted before McGurk sent a header over the bar.
It was Roberts who had the first decent chance from the edge of the box on 34 minutes, but his effort flew comfortably into the arms of Scott Loach.
Pompey did break the deadlock just before the break, however, thanks to an impressive solo goal from BENNETT.
The winger collected Enda Stevens’ pass down the left and beat Elliott Hewitt with ease before cutting inside and firing past Loach.
Notts County 0
The hosts probably should have doubled their advantage just after the restart, but McGurk somehow failed to connect with Davies’ free-kick from wide on the right.
But their second goal did arrive on 49 minutes – and it was a joy to behold.
Roberts displayed a moment of class to send BENNETT clear through and he calmly slotted the ball past Loach and into the net.
And Roberts then tried to add an audacious third with a cute lob from wide on the right that drifted narrowly over.
But the visitors were almost gifted a way back into the game on the hour mark when Jones dropped Curtis Thompson’s cross, only to pounce on the ball before Jon Stead could poke it home.
Pompey were soon back on the attack, though, and it took a brave block from former England international Alan Smith to deny his namesake Michael.
Cook made his first switch on 67 minutes, with the tiring McGurk making way for Naismith out wide.
With a comfortable lead, it was a more patient display from the hosts, but they still looked the more dangerous side.
And the home fans did have a third goal to cheer on 81 minutes when BURGESS converted Enda Stevens’ cross from close range to open his Blues account.
That was the cue to bring on Conor Chaplin and McNulty for the impressive duo of Smith and Roberts.
And it was McNULTY who wrapped up a memorable victory in stoppage-time when he headed Davies’ free-kick into the top corner.
Pompey (4-2-3-1): Jones; Davies, Burgess, Clarke, Stevens; Hollands, Doyle (c); McGurk (Naismith 67), Roberts (McNulty 84), Bennett; Smith (Chaplin 84)
Goals: Bennett 44, 49, Burgess 81, McNulty 90+1
Subs not used: Bass, Webster, Close, Evans
Notts County (3-5-2): Loach; Boyce (Atkinson 58), Smith (Campbell 75), Hollis; Hewitt, Thompson, Aborah (Burke 58), Noble, Milsom; McLeod, Stead (c)
Booked: Aborah, Milsom, Thompson, Smith, McLeod
Subs not used: Pilkington, Sharpe, Edwards, Murray
Referee: Michael Bull
Attendance: 16,670 (485 away fans)