Stade Franšais returned to the top of Pool 4 on Saturday thanks to a 15-13 win over Bath at Stade Jean Bouin.
Steve Meehan's side went into the Paris fixture knowing that only a win would do if they were to keep their slim Heineken Cup hopes alive.
And in cold and wet conditions they came close to fully capitalising on some charitable moments from the hosts, not least when full-back Lionel Beauxis handed them a try he will never forget.
Just three minutes before half-time, the French international chose not to catch a ball coming out from the back of a ruck and instead attempted to volley it downfield. It was a decision he would immediately regret as Michael Claassens duly pounced to pull Bath back from the brink.
That moment of madness best summed up the kamikaze nature of Stade at times and they will need to seriously up their game when their expected passage into the last eight arrives.
Paris had begun the game in their usual drop-oriented approach as Juan Leguizamon and then Ignacio Mieres had wayward shots.
Those attempts kept Bath on the back foot against the French runners but almost scored a breakaway try from their own 22 when Michael Stephenson - in a rare chance to prove his worth due to Nick Abendanon's injury - hacked and ran down the right to within ten metres.
In the end Mirco Bergamasco won the foot-race to save his side before interim full-back Joe Maddock went through a highly eventful five minutes of play that included two lows and one low. First the New Zealander dropped a high ball in the wet before later fumbling a grubber in behind the first line of defence, leading to his team-mates being offside and Beauxis opening matters.
However, Maddock demonstrated good character to respond with an excellent stepping run that moved Bath downfield and allowed Nicky Little to level the scores on 20 minutes.
Former England lock then Danny Grewcock riled the crowd - and a number of Stade players too - with a late hit on Arias that somehow went unpunished as the game continued to be a battle of attrition on a muddy pitch.
The Stade winger recovered to deal Bath a further blow by scoring his second try of the match, in the 34th minute, finishing off a free-flowing move on the right that involved James Haskell, Hugo Southwell and Dimitri Szarzewski.
But the visitors went into the break only five points behind thanks to that laughable play by Beauxis.
Fiji's most-capped fly-half then landed a 42nd-minute penalty as Bath closed to within two points at 15-13, which was how it stayed.
The pitch, especially its middle section, had cut up quite substantially by that stage so both sides' backs saw little of the ball out wide.
Stade were still dominating possession but Bath's close-quarter defence was strong, frustrating the home crowd, who became even more incensed when Beauxis missed a simple penalty attempt on the hour mark.
Little, who kicked all three of his shots at goal but less than impressive in other facets of his game, was replaced with eighteen minutes left as Ryan Davis came on in a late bid to prolong Bath's European adventure.
But there was not a try-scoring opportunity worthy of the name as Stade held out comfortably to go four points clear of Ulster at the top of the Pool. They just need to avoid defeat at Edinburgh next week to progress.
For Stade Franšais:
Tries: Arias 2
Stade Franšais: 15 Lionel Beauxis, 14 Julien Arias, 13 Mathieu Bastareaud, 12 Geoffroy Messina, 11 Mirco Bergamasco, 10 Ignacio Mieres, 9 Hugo Southwell, 8 Juan Leguizamon, 7 Pierre Rabadan, 6 James Haskell, 5 Pascal Pape, 4 Tom Palmer, 3 Sylvain Marconnet, 2 Dimitri Szarzewski, 1 Rodrigo Roncero.
Replacements: 16 Benjamin Kayser, 17 Rabah Slimani, 18 Pedro Ledesma, 19 Pierre Vigouroux, 20 Antoine Burban, 21 Aristide Barraud, 22 Guillaume Bousses, 23 Mark Gasnier.
Bath: 15 Joe Maddock, 14 Michael Stephenson, 13 Matt Carraro, 12 Shontayne Hape, 11 Matt Banahan, 10 Nicky Little, 9 Michael Claassens, 8 Luke Watson, 7 Jules Salvi, 6 Andrew Beattie, 5 Peter Short, 4 Danny Grewcock, 3 David Wilson, 2 Lee Mears, 1 David Flatman.
Replacements: 16 Pieter Dixon, 17 David Barnes, 18 Duncan Bell, 19 Stuart Hooper, 20 Ben Skirving, 21 Scott Bemand, 22 Ryan Davis, 23 Jack Cuthbert.
Referee: Alan Lewis (Ireland)
Assistant referees: Colin Stanley (Ireland), Kevin Beggs (Ireland)
Television match official: Marshall Kilgore (Ireland)