The Dragons relished the tag of underdogs to earn one of the greatest wins in their history, running in four tries in a stunning performance at Stade Jean Bouin.
The region had won in France just once in their history but upset the odds against the tournament favourites.
The Dragons headed into the game on the back of a pair of defeats to the Scarlets and Edinburgh but they rose to the occasion and produced their best display of the season.
They were rewarded for showing ambition and patience with ball in hand with scrum-half Richie Rees, hooker Rhys Thomas, wing Hallam Amos and flanker Nic Cudd scoring tries while half-backs Rees and Angus O’Brien pulled the strings expertly.
It was a real team effort if the Dragons can repeat the trick against Newcastle on Friday then they will fancy their chances of earning a spot in the quarter-finals.
The Dragons got their noses in front through the boot of O’Brien after four minutes but it came at a cost with Wales lock Andrew Coombs forced off after being taken out at a lineout.
But Stade Francais used their big pack to work their way into the game and fly-half Vincent Mallet rewarded their efforts with four penalties to earn a 12-3 lead after 25 minutes.
It looked like the Dragons would be up against it when loose head Boris Stankovich was yellow-carded for a high tackle.
However, they made light of their numerical disadvantage to strike twice to earn a 15-12 lead.
First lock Rynard Landman pounced on a loose ball and went on the charge before the ball was worked wide for centre Tom Prydie to go racing into the 22. He was tackled 10 metres shy of the line but scrum-half Richie Rees spotted a gap at a ruck to snipe over.
O’Brien’s conversion slammed against the pink left upright but he had better luck just four minutes later following Rhys Thomas’ score.
The hooker profited from a beautifully flighted pass by centre Ashley Smith following an impressive burst into the 22 by wing Matthew Pewtner.
The lead didn’t last long after Mallet banged over a leveller from halfway after Stade destroyed the Dragons’ scrum but the visitors would have been delighted to win the sin bin period 12-3 and head to the changing room on level terms.
And they were even happier eight minutes into the second half when flanker Lewis Evans stole a lineout and wing Hallam Amos raced over from 40 metres, beating last man Krisnan Inu with rather too much ease for the home side’s liking.
O’Brien converted and then added another three-pointer on 54 minutes to make it 25-15 – suddenly the Dragons were starting to dream of a stunning success.
But back came the hosts and after the forwards had hammered away at the line the ball was worked to the left for centre Herman Meyer Bosman to power over.
Morne Steyn converted but the Dragons responded with another O’Brien penalty earned at the scrum to make it 28-22 and that’s how it stayed until the 75th minute when the visitors’ young fly-half bisected the points to secure the victory.
But the visitors weren’t finished there and turned four points into five when openside flanker Nic Cudd darted over from close range.
Stade Francais: B Dumas (J Sinzelle 65), K Inu, G Doumayrou, H Bosman, D Ioane, V Mallet (M Steyn 47), J Fillol (J Tomas 63), Z Zhvania (B Dumas 71), R Bonfils (captain, A Oleon 47), D Kubriashvili (S Chellat 47), H Pyle, P Gabrillagues (J Nibert 61), M Ugena, M De Giovanni, N Garrault.
Scorers: try – H Bosman; conversion – M Steyn; penalties – V Mallet (5)
Dragons: L Byrne (captain), M Pewtner, T Prydie, A Smith, H Amos, A O’Brien, R Rees, B Stankovich (O Evans 48), R Thomas (E Dee 58), L Fairbrother (D Way 48), A Coombs (J Thomas 4, A Powell 52), R Landman, L Evans (O Evans 32-36), N Cudd, T Faletau.
Scorers: tries – R Rees, R Thomas, H Amos, N Cudd; conversions – A O’Brien (3); penalties – A O’Brien (4)
Referee: Luke Pearce (England)