A Guy Whittingham hat trick sentenced Port Vale to their 10th successive away defeat and their midfielder Neil Aspin was sent off to complete a dismal afternoon for Vale boss Brian Horton.
Whittingham, on loan from Sheffield Wednesday, tormented the Vale defence all afternoon and displayed his lethal finishing with two goals before half time and a third a minute before the end.
Alan McLoughin gave Portsmouth the lead after 29 minutes from the penalty spot after Tony Rougier brought down Matthew Robinson with a clumsy tackle inside the box.
McLoughin's shot beat the dive of Paul Musselwhite who chose the right way but was powerless to keep out the effort from the Republic of Ireland International.
Frenchman Jeff Peron was the inspiration behind the start of Whittingham's rout, sending in a perfect cross from a 36-minute corner which caused chaos in the Vale defence.
There was no one marking Whittingham as he stooped to beat Musselwhite with an accurate header.
Three minutes later former soldier Whittingham grabbed his second, meeting another cross from Peron with a powerful header at the far post.
Whittingham completed his hat trick after exchanging passes with John Durnin in the last minute of the game and smashing a left-footed shot into the roof of the net.
Vale midfielder Aspin was booked in the 56th minute for a foul on Peron and referee Hall had no option but to send him off when he clumsily bundled over Steve Claridge after 76 minutes.
To make matters worse for Vale they lost leading scorer Martin Foyle after just 14 minutes of the game when he limped off with a knee injury to be replaced by substitute Wayne Corden.
Horton's side had their only real chance in 50th minute when Pompey's Greek International Michalis Vlachos brought down Craig Russell on the edge of the penalty area.
Russell got to his feet and let fly with a powerful left shot which flew just inches over Alan Knight's crossbar.
There were also bookings for Vale's Paul Beesley, Tony Rougier, and substitute Michael Walsh. Robinson was booked for Portsmouth but Alan Ball's side continued this year's unbeaten run.