Piquionne scored one goal and made the other in a scintillating three-minute first-half spell to set Pompey on course for a much-needed first win of the season.
The home side looked primed for a giantkilling after another week of turmoil at Fratton Park, capped by captain Sylvain Distin asking for a move prior to kick-off.
Piquionne gave Paul Hart's side the perfect start by firing past Bulls goalkeeper Adam Bartlett from 12 yards with only 20 minutes gone.
Man of the match Piquionne, who had already smashed an earlier effort against a post, turned provider moments later, crossing for John Utaka to sweep home Pompey's second.
Niko Kranjcar put the game beyond Hereford's reach two minutes before half-time when his 20-yard shot squirmed under the unlucky Bartlett to make it 3-0.
Hereford, third from bottom in the Football League, were targeting a repeat of their famous 1972 FA Cup win over then First Division Newcastle.
But Richard Hughes wrapped up a comfortable victory 11 minutes into the second half with a spectacular strike to claim his first goal since February 2004.
Former Scotland midfielder Hughes swivelled on the edge of the penalty area before picking out the top right corner with an unstoppable left-foot curler.
The 700 travelling Hereford fans, among a sparse crowd of only 6,645 at half empty Fratton Park, finally had reason to cheer just past the hour mark.
Stand-in Pompey goalkeeper Asmir Begovic was harshly adjudged by referee Andy D'Urso to have tripped Tristan Plummer and the Bulls striker smashed the resulting spot-kick into the left corner.
Substitute David Nugent should have made the win more emphatic in the dying minutes after racing through one-on-one with Bartlett but shot straight at the grateful keeper.