Paris - George Ford missed a last-gasp penalty for Bath as Stade Francais won 28-25 on Sunday to reach the European Challenge Cup final.
Jules Plisson had given Stade the lead in Paris with a nerveless drop goal 30 seconds from the end of a pulsating match.
It wasn't finished there, though, as Bath piled forwards and forced a penalty -- yet from wide out on the left, Ford missed and Stade will play Gloucester in the Edinburgh final on May 12.
Gloucester beat French Top 14 leaders La Rochelle 16-14 on Saturday night.
Stade and Bath put on a stunning display of attacking rugby at the Jean Bouin stadium in the French capital and the most dramatic of finales.
Yet there was little indication in the first half of what would come later as Stade took control early on through Geoffrey Doumayrou's try that helped them to an 11-6 half-time lead.
Plisson took a perfectly weighted pass from Australian international scrum-half Will Genia to score under the posts on 48 minutes, converting to give Stade an 18-6 lead.
Bath were wobbling but when the fightback started it quickly built momentum as they swung the ball from side to side probing for an opening.
Fijian-born British soldier Semesa Rokoduguni was twice given a one-on-one chance against Stade Francais full-back Hugo Bonneval.
The first time the wing was smothered by covering defenders but the second he side-stepped the Frenchman and cantered over in the right corner on 63 minutes.
Bath were now in total control and created space on the opposite wing where New Zealander Robbie Fruean bulldozed through a desperate diving tackle by Genia to score.
Ford missed the conversion leaving the scores level at 18-18 but he would have another chance to transform five points into seven immediately afterwards.
More Bath pressure saw Stade crack all too easily and replacement lock Elliott Stooke strolled over under the posts.
Ford's conversion meant Bath had turned a 12-point deficit into a seven-point lead in just eight minutes.
But two minutes from time, Stade broke from inside their own 22 with Djibril Camara brushing off a weak tackle by Anthony Watson and then passing inside for Australian lock Hugh Pyle to sprint 50 yards and score.
Plisson dissected the posts and it was all square again.
Stade regained the ball from the restart and drove straight up the field for Plisson to knock over the winning points.
Yet still the game wasn't over, Bath reclaiming the restart and after Watson and Rokoduguni failed to turn a two-on-one chance into a try, Stade gave away a penalty.
Nerves of steel were required but Ford's effort faded to the right and Stade's celebrations began.
On Saturday, Billy Burns scored all of Gloucester's points to inflict a first home defeat of the season on La Rochelle.