A powerful charge upfield by the impressive Matt Banahan helped set the platform for Little to orchestrate the try, which the fly-half finished off from close range after Shontayne Hape had punctured the Stade defence.
And five minutes later Banahan's threat, which drew the attentions of three Stade backs, allowed the winger to find Carraro in space with a simple pass and the Australian galloped over Hugo Southwell to put Bath 13-6 up.
Little converted Carraro's try and kicked three first-half penalties, but Dupuy slotted three penalties of his own to keep Stade within nine points at the interval.
The second half was in complete contrast to the open nature of the first 40 minutes.
Pascal Pape was sin-binned for kicking the ball out of Bath skipper Michael Claassens' hands, but the home side could not make their numerical advantage count.
Bath were then forced to close ranks themselves after Banahan was sent for 10 minutes in the sin-bin for clattering into Mirco Bergamasco, but the visitors only improved their tally by a couple of Dupuy penalties by midway through the half.
Little responded with two penalties of his own to keep Bath six points clear, but exquisite handling by Southwell put Phillips clear down the left with time running out and he outsprinted Nick Abendanon in the race for the corner to pull Stade within a point.
The normally reliable Dupuy pushed his conversion though and it looked as though the home side would hold on for a crucial victory until the Stade scrum-half was given one final opportunity from just inside the Bath half.
It is the second successive season that Dupuy has ruined Bath's Heineken Cup hopes. In April, the Frenchman scored a late try for Leicester in their 20-15 quarter-final victory.
Bath coach Steve Meehan:
"We are going to have to play very well in our remaining four games and hope other results go our way.
"I won't be too hard on the players. It is obviously very disappointing for all of the guys.
"Unfortunately, we were penalised a couple of times too often, and perhaps we went away a little from how we played in the first half.
"But we played a much better brand of rugby than we did against Ulster last week, and we will continue to try to develop that."
Stade's England lock Tom Palmer: "Stade have been in two European finals and lost them both.
"There is a huge desire within the squad to put that right. The final being in Paris is a real motivating factor.
"Away wins in the Heineken Cup are so important. If you can do that, while also winning your home games, then you are in charge of your pool."
Bath: Abendanon; Maddock, Carraro, Hape, Banahan; Little, Claassens; Flatman, Dixon, Bell, Hooper, Grewcock, Faamatuainu, Salvi, Skirving. Replacements: Cuthbert for Maddock (77), Barnes for Flatman (69), Hawkins for Dixon (60), Wilson for Bell (60), Short for Grewcock (77), Cracknell for Faamatuainu (70). Not Used: Bemand, Davis.
Sin Bin: Banahan (53).
Stade Francais: Southwell; Arias, Bousses, Messina, Gasnier; Beauxis, Dupuy; Roncero, Szarzewski, Attoub, Palmer, Pape, Haskell, Rabadan, Parisse. Replacements: Phillips for Arias (50), M Bergamasco for Messina (30), Blin for Szarzewski (67), Gerber for Attoub (55), Kayser for Rabadan (50). Not Used: Weber, Marchois, Oelschig.
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