It is the first time this season any Portsmouth frontman has netted in the league.
Portsmouth should have taken the lead in the 26th minute when Dindane headed Kevin Prince Boateng's header over the crossbar after colliding with Piquionne.
Wigan goalkeeper Chris Kirkland found Piquionne's 29th minute piledriver too hot to handle, but reacted well to gather the rebound before Jamie O'Hara could pounce.
Dindane made amends for his earlier miss with a well-taken opener ten minutes before half-time.
Algerian midfielder Hassan Yebda sliced the Wigan defence in two with a slotted through ball and Dindane neatly lifted the ball over the onrushing Kirkland and into the bottom left corner.
Portsmouth doubled their lead on the stroke of half-time as Piquionne burst into the penalty area down the right and placed an angled shot into the opposite corner.
Dindane put the match out of hopeless Wigan's reach early in the second half, sliding in to finish from close range, after substitute Kanu and O'Hara had combined down the right.
Ivory Coast international Dindane completed the rout from the penalty spot in the final minute.
Kanu was tripped by Emmerson Boyce and Dindane stepped up to hammer the resulting sot-kick into the roof of Kirkland's net.
The only sour note for Pompey was Piquionne being stretchered off midway through the second half after landing awkwardly on his knee.
Wigan, who also saw in-form Hugo Rodallega hobble off after falling over advertising boards, did not muster a single shot on target.
Midfielder Hendry Thomas's header high over David James' crossbar was the closest Roberto Martinez's side came to getting on the scoresheet.