Edinburgh 15 (3)
Elissalde kicked 14 points for Toulouse at Murrayfield
Tries: De Luca, Houston
Pens: D Blair
Toulouse 19 (9)
Pens: Elissalde 4
Edinburgh pushed Toulouse all the way to earn a creditable losing bonus point after a brave display at Murrayfield.
Jean-Baptiste Elissalde kicked an uninspired Toulouse to a 9-3 half-time lead as Edinburgh's defence frustrated their illustrious visitors.
Maxime Medard scored for Toulouse, but Nick de Luca and John Houston brought Edinburgh back to just a point behind.
Elissalde put Toulouse four points up, and Edinburgh's desperate attempt to score a winning try came up just short.
In a tight group also containing Leinster and Leicester, Toulouse would have hoped to have left Edinburgh with something more than a four-point win, but they were fortunate to avoid defeat after a lacklustre display.
Two early penalties from Elissalde put Toulouse 6-0 up as they tried to make their class tell by playing with plenty of width to stretch the Edinburgh defence.
Young Edinburgh fly-half David Blair replied with a kick of his own, but Elissalde restored his side's six-point lead with a 25th-minute kick.
Edinburgh won a string of penalties for Toulouse offences at the scrum, destroying any sense of attacking momentum for the visitors.
Blair missed with a late penalty attempt, but Edinburgh went into the half-time break knowing they were very much in the match against a lackadaisical Toulouse.
The French side finally found a way through early in the second half after an intelligent offload from Yannick Jauzion put Gaffie du Toit into space down the blind side.
Du Toit found the supporting Medard with a pop pass and the winger outpaced Andrew Maxwell to dot down next to the posts.
Edinburgh refused to roll over though, and gained a one-man advantage when Elissalde - who received the unwanted attention of Ben Gissing's boots for his troubles - was sin-binned for cynically killing the ball.
After going through 10 phases, Edinburgh swung the ball out to the left and centre De Luca showed great footwork to stand up Jauzion and cross the Toulouse line.
Edinburgh repeated the trick on 68 minutes when substitute Houston cut a great line off a Ben Cairns pass, leaving Clement Poitrenaud on his backside on his way to the try-line.
Phil Godman's excellent conversion cut Toulouse's lead to just one point, and panicked Toulouse into a couple of unsuccessful long-range drop-goal attempts.
Elissalde made amends for his yellow card with a penalty to take Toulouse clear again, and a frantic final few minutes from Edinburgh failed to breach their opponents' defence.
Edinburgh coach Andy Robinson:
"The attitude was there but the team needs to know we are not here to come second.
"The frustrating thing for me is that this was a game we should have won.
"There is a tremendous attitude, real enthusiasm and vibrancy, and I feel sorry for them after that. They have put in a real effort."
Toulouse coach Guy Noves:
"That was not our best ever display - and all credit to Edinburgh for making
life so difficult for us, just as we knew they would.
"We have faced them many times over the past few years - and particularly at home, they are always a handful.
"We have a lot to think about and a lot of work to do before we take on
Leinster next weekend."
Edinburgh: Hugo Southwell, Andrew Turnbull, Ben Cairns, Nick De Luca, Andrew Maxwell, David Blair, Mike Blair, Allan Jacobsen, Ross Ford, Gavin Kerr, Craig Hamilton, Ben Gissing, Allister Hogg (capt), Ross Rennie, Simon Cross.
Replacements: Andrew Kelly, Augusto Allori, Matt Mustchin, David Callam, Ben Meyer, Phil Godman, John Houston.
Toulouse: Poitrenaud, Clerc, Jauzion, Mermoz, Medard, Du Toit, Elissalde, Maka, Dusautoir, Nyanga, Albacete, Lamboley, Montes, Servat, Perugini. Replacements: Courrent, Bouilhou, Sowerby, Kunavore, Millochluski, Poux, Basualdo.