Seven penalty kicks from Jonny Wilkinson had the European champions 21-15 ahead in the dying embers of play.
However, the former England hero saw a pass intercepted by Alipate Raitini, who went on to score a dramatic try.
The conversion, successfully taken by Julien Caminati, sealed a first defeat at home for Toulon in just a day shy of a full year.
With Castres winning on Friday and league leaders Clermont playing Toulouse on Sunday, the defeat looks set to see Toulon lose ground in the four-way battle for the league summit.
Meanwhile the win for Grenoble- their ninth of the season - lifts them up to 5th momentarily in the Top 14.
Elsewhere, Stade Francais won 18-6 at Biarritz to go second; Oyonnax defeated Racing Metro 6-0 in a low scoring contest; Perpignan enjoyed a 20-8 win over Bayonne and Brive defeated Montepellier 15-9.