Goals from Conor Chaplin, Gary Roberts, Carl Baker, sub Milan Lalkovic and Danny Rose saw the Blues return to winning ways in style and keep up their unbeaten home record.
Paul Cook’s side had to come from behind to do that, though, after John Akinde put the Bees in front from the penalty spot in the first half.
Roberts also missed a second-half penalty as Bira Dembele pulled down Chaplin in the box and was dismissed.
It was an entertaining affair from start to finish in front of 16,280 fans at Fratton Park.
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Barnet played their part in that but could do little to contain Pompey’s attacking might as the game wore on.
The result also lifts Pompey to second in the table and will go down as one of the most impressive results of the Cook era.
It proved an eventful and entertaining first 45 minutes at Fratton Park.
Pompey started well but had David Forde to thank for an alert charge from his box to deny the on-rushing John Akinde after 10 minutes.
Baker had a great chance three minutes later from Gareth Evans’ cutback, but he fired over from 10 yards with the ball just behind him.
Curtis Weston then got around Forde but was forced wide and Christian Burgess cleared his shot.
Tom Davies then should have done better from Gary Roberts’ corner, but allowed the ball to hit him rather than attack it and Josh Vickers gathered.
The opener came in disputed fashion after 27 minutes when ref Darren England ruled Davies handled in the box as he cleared a free-kick.
There were protests from the defender and Forde but Akinde dispatched his penalty under the keeper’s dive to his right.
The reply arrived seven minutes later with Roberts the architect with a majestic no-look pass into Chaplin’s path - allowing the teenage striker to finish with aplomb from a few yards out.
Gareth Evans then showed real desire to attack the ball at the back post just before the break. The ball dropped to Baker whose shot was blocked and Chaplin acrobatically fired the follow-up wide.
The pace didn’t let up after the break with Christian Burgess making an important early tackle to deny Jamal Campbell-Ryce.
But two goals in six minutes then saw the pendulum swing in Pompey’s favour.
The first arrived moments after Roberts passed up a gilt-edged chance from Enda Stevens’ cross as he totally missed the ball from six yards.
It didn’t faze Pompey’s talisman though, as he then beat Michael Nelson and stuck a finish past Vickers with the outside of his left boot from 12 yards.
Pompey’s third arrived after 56 minutes via the quality of Baker. The attacking talent drifted into the box and curled a left-footed shot past Vickers to put daylight between the sides.
Barnet were then reduced to 10 men after 65 minutes when Dembele brought down Chaplin in the box.
Roberts was the man who stepped up but his thumped spot-kick was well pushed away to safety by Vickers.
The fourth goal did arrive though, after 78 minutes as sub Lalkovic confidently buried a finish from the edge of the box.
And Rose put the icing on the cake in stoppage time as he danced through the Barnet defence and slotted the ball under Vickers at the end of a flowing team move.