Edinburgh progressed to the Heineken Cup Semi-finals after they beat former Champions Toulouse 16-14 at Murrayfield on Saturday.
Edinburgh are the first Scottish team to reach a Heineken Cup Semi-final.
Edinburgh did it the hard way having at one point being reduced to 13 men in the first-half but 14 points from man of the match Greig Laidlaw inspired them to a memorable victory against a surprisingly under-par French outfit.
Edinburgh's victory at Murrayfield will come as a great antidote to the disappointment of the national side ending with the Six Nations wooden spoon.
Edinburgh, who in their only previous quarter-final against Toulouse in 2004 were thrashed 36-10, will play the winners of Munster and Ulster, who play on Sunday, in Dublin on April 28.
"Hopefully it's the big pick me up that we all need," said Laidlaw. "It just shows that with the crowd as well there is the support for us.
"It will be a tough shift that semi-final agaisnt Irish opposition in Dublin."
Edinburgh got off to a terrific start and rewarded the almost 40,000 crowd with a try inside the first two minutes as Mike Blair squeezed over after Laidlaw's high ball had not been gathered by Timoci Matanavotu.
Referee Nigel Owens called for the video referee and he gave the nod for the scrum-half's fourth European Cup try - Laidlaw converted for 7-0.
Two penalties from France fly-half Lionel Beauxis reduced the deficit to 7-6 after 20 minutes before the hosts threatened to implode when they were reduced to 13 men.
First veteran prop Allan Jacobsen, one of the few survivors from the 2004 quarter-final, and then backrow forward Ross Rennie were yellow-carded in the 25th and 26th minutes.
Beauxis rubbed salt into the wound by slotting over a penalty to give the visitors a 9-7 lead.
Toulouse added to their lead with a wonderful solo try from Fijian flier Matanavotu, who ran the ball back from the halfway line, brushing aside three tackles, for his eighth try of this year's tournament and taking him to within one of the record.
Beauxis missed the conversion and Edinburgh reduced the deficit when Laidlaw dropped a superb drop goal from long range two minutes from the break to send them in only 14-10 down.
Toulouse made the worst possible start to the second-half with experienced former France hooker William Servat, playing in his eighth quarter-final for his club, yellow-carded.
Laidlaw converted the resulting penalty and added another in the 52nd minute to send them into the lead at 16-14 and added one in the last minute to crown a superb team and personal performance.
Final Score Edinburgh 19 (10) Toulouse 14 (14)
Penalties: Laidlaw 3
Penalties: Beauxis 3
Referee: Nigel Owens (Wales)
Edinburgh Rugby: T Brown; L Jones, N De Luca, M Scott, T Visser; G Laidlaw [capt], M Blair; A Jacobsen, R Ford, G Cross, G Gilchrist, S Cox, D Denton, R Rennie, N Talei
Replacements: A Kelly, K Traynor, J Gilding, S McInally, R Grant, C Leck, P Godman, J Thompson
Toulouse: Y Jauzion; T Matanavou, F Fritz, Y David, Y Donguy; L Beauxis, L Burgess; J Poux, W Servat, C Johnston, Y Maestri, P Albacete, J Bouilhou, T Dusautoir [capt], L Picamoles
Replacements: C Tolofua, D Human, Y Montes, G Lamboley, J Doussain, C Poitrenaud, Y Nyanga, G Galan