Instead, Glasgow left with a stunning 33-26 victory thanks to tries from centre Graeme Morrison, flanker Kelly Brown and wing Max Evans, along with 18 points from the boot of fly-half Dan Parks.
Glasgow, who were propping up Pool 5 with four successive Heineken Cup defeats prior to Saturday's historic win, raced into a 23-3 half-time lead as Toulouse failed to live up to their pre-match billing as one of the tournament favourites.
The French side closed the gap through two penalties from Jean-Baptiste Elissalde but Glasgow led 33-9 with just 10 minutes remaining courtesy of Evan's opportunistic try and a further five points from Parks.
Although the 1996, 2003 and 2005 champions gave themselves late hope through a penalty try and another from Gaffie du Toit, it wasn't enough to spoil the Glasgow party.
Elsewhere in Pool 5, Bath claimed a narrow win over Newport Gwent Dragons at Rodney Parade to take control of the group with just one round remaining.
Tries from Richard Fussell and Wayne Evans looked set to earn the Dragons the four points after Joe Maddock had opened the scoring for the visitors but a Stuart Hooper effort ensured Bath made the short journey home with a valuable win.
That result means a win for Bath over Toulouse next weekend will leave the French outfit relying on an unlikely best runners up spot to make it through to the last eight.
Heineken Cup results, round five
Friday, January 16
Edinburgh 32 Castres 14
Munster 37 Sale 14
Clermont 43 Montauban 10
Saturday, January 17
Ulster 21 Harlequins 10
Calvisano 15 Biarritz 23
Toulouse 26 Glasgow 33
Leicester 52 Treviso 0
Perpignan 17 Ospreys 15
Wasps 19 Leinster 12
Sunday, January 18
Dragons 12 Bath 15
Gloucester 12 Cardiff Blues 16
Scarlets 31 Stade Francais 17