Radamel Falcao and Kamil Glik scored second-half headers which proved decisive on Friday after the visitors had threatened to cause a major upset.
Mbappe, heavily linked with a move away during the transfer window, was not among the scorers and limped off with an injury Leonardo Jardim, as well as the striker's suitors, will hope is not serious.
Toulouse took a shock lead after only six minutes, a clever corner routine seeing Corentin Jean find Andy Delort outside the box, with the striker sending a clever chested pass into the area that allowed Zinedine Machach to produce a first-time finish past Danijel Subasic.
Mbappe had a shot saved by Alban Lafont after Rony Lopes' throughball, but Monaco levelled after 28 minutes when Joao Moutinho swung in a corner from the left and Jemerson rose well to head in from six yards for a rare goal.
Lafont was at full stretch to keep out Thomas Lemar's free-kick early in the second half, which proved crucial when Toulouse moved back in front after 53 minutes. Djibril Sidibe lost possession led to Jimmy Durmaz, who found Delort to send a low shot past Subasic from 20 yards.
Monaco levelled within five minutes. A clever flick from Mbappe, who previously had a penalty claim rejected, set up a left-wing cross from Jorge for Falcao, whose close-range header was too powerful for Lafont to keep out.
Moutinho then got his second assist of the night after 70 minutes, lofting in a free-kick which Glik got the faintest of touches to at the far post, a goal that proved to be the winner.
Mbappe gingerly walked off the field with 15 minutes remaining after signalling he wanted to be replaced during a break in play. His replacement, Allan Saint-Maximin, set up fellow substitute Guido Carrillo to test Lafont in stoppage time as the champions settled for a narrow victory in an exciting start to their title defence.