They remain top of Pool 5 for now but that will almost certainly change tomorrow when Harlequins play basement side Timisoara, and will be expected to take all five points.
As is often the case with Top 14 sides who have their eye on the more lucrative domestic competition, the French outfit may be taking the competition less seriously than some of their rivals. However, the back-to-back fixtures against Edinburgh offered an opportunity to build momentum.
And with the backlash from last week’s second-half collapse adding further impetus, there was no doubting their hunger to succeed.
That was evident in the early exchanges, when Stade piled on the pressure. Edinburgh lost the first scrum and conceded a penalty at the second. And their problems grew when a penalty was despatched into touch and from the ensuing lineout, Remi Bonfils, the home hooker blasted his way in for a try, which was converted by Jules Plisson.
Edinburgh thought they had replied in kind when Ben Toolis scrambled over. However, the video official decided it had been a double movement.
With 15 minutes on the clock, Edinburgh opened their account when Jason Tovey kicked a penalty following an offence at the breakdown.
The hosts struck back almost immediately with a powerful run from Josaia Raisuqe, with the ball spun along the line to Sergio Parisse who fed Hugo Bonneval for an unconverted touchdown.
Things got worse for the Scots when Stade were awarded a penalty for Blair Kinghorn diving on tackled player. They opted for the scrum and a powerful surge left the referee no option but to award a penalty try and yellow card Simon Berghan. Plisson added the extras from in front of the posts.
By half-time, the hosts had secured the bonus point after Jeremy Sinzelle freed Geoffrey Doumayrou. Plisson again converted for a 26-3 interval lead although the hosts reached the end of a 50-minute first half with only 14 players after Sylvain Nicolas was yellow carded.
The visitors must have been hoping for a repeat of the Frenchmen’s second-half capitulation seen at BT Murrayfield five days earlier. And they raised aspirations of such an outcome within two minutes of the restart when Hamish Watson was hauled down just short of the line but Fraser McKenzie followed up and dived over for the score.
That touchdown appeared to have been cancelled out in 57 minutes when Plisson stepped inside and darted through a gaping hole in the Edinburgh defence. However, after reviewing the lead-up several times, the referee ruled it out for a dangerous tackle.
Kinghorn almost took advantage when he dodged his way past three defenders. But, as he dived over the line, Raisuque dislodged the ball. The score was only delayed a couple of minutes and it came through Viliame Mata, whose first involvement after entering the fray was to blast through three tackles on his way to the line, Tovey added the extras.
And Edinburgh gave themselves a glimmer of hope when Sam Hidalgo-Clyne, who had moved to the left wing, darted in for an unconverted try a minute from the end.
One final assault on the French defence had a nervous home crowd shouting for the final whistle. And there was relief for the hosts when the move ended with a knock on.