Steve Cotterill claimed before the game that his side were due to hand out a thrashing to someone - and they proved him right in style.
Liam Lawrence tucked away an early penalty and doubled the lead with a deflected free-kick to put Pompey in charge at half-time and the one-way traffic continued after the break.
Dave Kitson grabbed a brace, David Nugent scored his first league goal of the season and Michael Brown rounded off the victory with a fine sixth as Pompey's luck finally turned for the better.
The south-coast club, who remain in administration and still cannot fill their substitutes' bench, have been swimming against the tide all season.
But a combination of Michael Morrison's ridiculous handball and referee Keith Hill's harsh decision to send off Portuguese defender Miguel Vitor put them on their way to a much-needed win.
Morrison gifted them the lead after just nine minutes when, for reasons best known to himself, he raised his arm as he jumped for Lawrence's corner.
Hill pointed to the spot and Lawrence stepped up to send Conrad Logan the wrong way.
Leicester tried to hit back immediately and had the ball in the net in the 17th minute, but Andy King was adjudged to be offside when he tucked Lloyd Dyer's pass away.
However, Pompey were dominating possession and Lawrence saw an angled shot tipped over by Logan, Michael Brown fired narrowly wide and Aaron Mokoena sent a volley over.
And Leicester's evening got worse on the half-hour when Vitor was dismissed for felling Nugent on the edge of the area.
While it was a clear foul, their were plenty of other defenders in attendance and Vitor was stunned to see Hill produce the red card.
Lawrence rubbed salt in the wounds when he thumped the free-kick past Logan with the help a deflection off Bruno Berner.
Carl Dickinson almost scored a memorable goal just after the break with a 30-yard effort from the left touchline which caught Logan off his line but his effort just shaved the crossbar.
But moments later Pompey did grab the third when Logan palmed Kitson's shot to the feet of Nugent.
The former Burnley striker's initial effort was blocked by Logan but he kept his head to slot in the rebound from a tight angle.
And straight from the restart Pompey were four up, Nugent winning the ball back and playing in Kitson to chip over Logan and into the net.
Steve Howard bundled in a consolation from a goalmouth scramble, but some more generous defending allowed Kitson to tap in number five.
And Brown capped a memorable night with a stunning solo effort in the last minute as some of the gloom finally began to lift around Fratton Park.