A USEFUL Albion debut from Youssouf Mulumbu wasn't enough to save Michael Appleton's men from a third successive defeat.
The Baggies were gunned down by a fine hat-trick from Thomas Kilbey.
The hosts dominated the first 45 but conceded on the stroke of half-time.
They were less impressive after the break and duly conceded twice more.
Mulumbu fulfilled his defensive midfield role with aplomb on his first outing in an Albion shirt since joining on loan from Paris Saint Germain in January.
But his performance was still eclipsed by that of sidekick Graham Dorrans, who really caught the eye during a 68-minute workout.
Albion started well and Juan Carlos Menseguez and Seb Lake-Gaskin both went close during the opening ten minutes.
Luke Moore then tested Pompey keeper Jamie Ashdown from 18 yards before heading a Lake-Gaskin centre just over.
It was all Albion and Lake-Gaskin saw a fierce drive deflect behind off defender Martin Cranie.
Moments later, centre-back Paul Downing headed wide from a corner.
After Pompey's Marlon Pack headed a left-wing free-kick straight at Dean Kiely on 29, Do-heon Kim, twice, and Menseguez peppered the visitors' goal with decent efforts.
Out of the blue, the South Coast side rattled the angle of the Baggies' post and bar on 42 when Gautier Mahota unleashed a 25-yard free-kick.
And, against the run of play, Portsmouth opened the scoring seconds before the half-time whistle when Pack headed a corner back across goal for Kilbey to nod home his first.
Albion failed to reach the same heights after the break and Downing had to hook clear after Kiely spilled James Hurst's shot.
The Baggies broke upfield and Menseguez raced onto Lake-Gaskin's fine crossfield ball before shooting just wide of the far post.
On 66, Albion were two down when Pack again teed up Kilbey, who drilled home from the edge of the box
Carl Hoefkens wasn't too far away with a volley from Lake-Gaskin's corner before Menseguez was denied by Ashdown's fine save.
Pompey sub Daniel Bogard should have added a third on 84, only to fire over from a couple of yards when it looked easier to score.
But the visitors did net again in stoppage time when Kilbey completed his treble with a cool ten-yard finish.
ALBION (4-2-3-1): Kiely; Samuels, Hoefkens, Downing, Martin; Mulumbu, Dorrans (Wood 68); Lake-Gaskin, Kim (Labadie HT), Menseguez; Moore (Bednar HT). Subs not used: Gayle, Knight.
PORTSMOUTH: (4-4-1-1): Ashdown; Hurst, Cranie, Wilkinson, Blackman; Nlundulu, Pack, du Chattelier (Bogard HT), Mahoto (Cuvelier 77); Kilbey; Navas Alors (M Smith 77). Subs not used: O'Brien, Mantyla.
GOALS: PORTSMOUTH - Kilbey (45+1, 67 & 90+1).
REFEREE: R Wigglesworth.
ATTENDANCE: 355.
ALBION STARMAN: Graham Dorrans.