Perpignan were French champions in 2009 but are struggling in the Top 14 this season, with poor home form hampering their cause.
However, after a nervous start they slowly gained the upper hand in glorious sunshine and balmy 20C temperatures just inland from the Mediterranean coast.
A superb scrummaging performance from the hosts' pack was at the heart of their performance and the edge they gained up front was enough to set up their second win in Pool Five.
And such was the pressure exerted in the tight that Leicester were forced to withdraw highly-rated young England tight-head Dan Cole in favour of Italy cornerstone Martin Castrogiovanni at half-time.
Leicester fly-half Flood, back after a week on the sidelines following the head injury he sustained in England's Test against world champions South Africa, popped over a third-minute penalty to give the visitors the lead.
Porical was short with a long-range penalty attempt for the hosts but levelled matters when Perpignan - not for the last time - got the better of the much-vaunted Tigers pack at a scrum.
However, Flood soon edged Leicester back in front and Porical then missed a simple effort just after the half hour mark, before the hosts found themselves down to 14 men.
A Matt Smith break saw Leicester surge to within a couple of metres of the hosts' line and when Ben Youngs looked to move the ball wide his pass cannoned into the off-side David Marty.
The centre was duly sin-binned and Flood gave the Tigers a 9-3 lead, which Porical reduced by three after Perpignan again won a penalty at the scrum.
With half-time looming Perpignan were awarded the put-in at a series of five-metre scrums on the Leicester line.
Referee Alan Lewis eventually lost patience and sin-binned hookers Marius Tincu and George Chuter and when the hosts finally released the ball to the backs, Nicolas Laharrague's cross-kick was well finished off by Plante, who side-stepped Murphy to score in the corner.
Porical found his kicking boots to convert and send Perpignan in 13-9 up at the break.
Leicester turned to Castrogiovanni to try and shore things up in the front row but they fell further behind 10 minutes after the re-start when Porical raced 40m after wrong-footing Murphy for a fine unconverted try in the corner.
But Leicester rapidly hit back as a Smith block enabled Scott Hamilton to break through the midfield and put Murphy over in the corner.
Flood converted and the Tigers were only two points down with more than a quarter of the game still to play.
The England number 10 could have put Leicester back in front but he pulled a long-range penalty wide of the posts and two further penalties from Porical looked like sending Leicester home empty handed from their trip to the south west of France.
However, Flood moved the Tigers back within seven points with his fourth successful penalty, and they rode their luck in the closing seconds.
Porical, with a penalty, and David Mele, with a snap drop-goal, both missed kicks which would have denied Leicester what could prove to be a vital losing bonus point.
Leicester director of rugby Richard Cockerill: "We had the belief to come here and win but we made a few errors that cost us and they are a dangerous side.
"The spirit and stubbornness of the players was excellent, especially in that spell where we were under severe pressure at the end of the first half. You can't coach that. It is one of the positives we will take from the game.
"We had to come away with at least a point. We didn't want to go back home with nothing because this is such a tight group and every point will count for something in the end."
Perpignan director of rugby Jacques Brunel: "We are very pleased with this win. We have not had good results recently in the league but Europe is still important to us and we are very happy to beat a team of the reputation of Leicester."
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