Julien Dupuy returned to ruin Bath's Heineken Cup ambitions for a second successive season as Stade Francais stole a dramatic 29-27 Recreation Ground victory.
The scrum-half's seventh penalty a minute from time condemned Bath to their second successive Pool Four defeat.
No team has reached the quarter-finals after losing their opening two group games, but that is the colossal challenge now facing Bath.
Dupuy's late try for Leicester last term sent Bath crashing out at the quarter-final stage, and he again ruthlessly punished them.
Home wing Matt Banahan had earlier run riot, the 6ft 7in England wing repeatedly blasting through Stade's defence.
His line-breaking prowess from broken field play was showcased spectacularly as he warmed up for England's autumn Test series that starts against Australia on November 7.
A second-half yellow card looked as though it would not spoil Banahan's afternoon, given that Bath had already capitalised on his dynamic contribution through tries for fly-half Nicky Little and centre Matt Carraro.
Little also booted one conversion and five penalties for a 22-point haul, yet Bath were forced to desperately hang on before Stade substitute and England sevens star Ollie Phillips touched down after 76 minutes.
Dupuy then required only one more opportunity to nail the win and it duly arrived in the closing seconds of a gripping encounter.
Scotland won three matches in this year's Championship
24 March 2017, 3:33pm
Scotland secured three RBS 6 Nations victories for the first time since 2006 as they beat Ireland, Wales and Italy at BT Murrayfield. Here we take a look at what lies ahead for the Scots in the next 12 months.
Peter Malone has been Nigel Carolan's assistant since 2015
24 March 2017, 11:56am
The IRFU have announced Peter Malone as the Ireland Under-20s interim head coach for the World Rugby Under-20 Championship in Georgia this summer after Nigel Carolan announced he would take a position at Guinness PRO12 side Connacht.