Helder Rodrigues won Saturday's penultimate stage 13 but it was Despres who had the biggest reason to smile at the end of the day, as gearbox problems for overnight leader Marc Coma saw him make up 12 minutes 38 seconds and open up an 11 minutes and three second-margin at the front.
Despres came in 47 seconds behind Rodrigues' time.
Despite his good fortune, Despres kept his joy in check after the stage.
"I am not the kind of person who derives pleasure from the problems of team-mates, and even less when it is Marc Coma who is in trouble," he said.
"Today's stage was psychologically very tough. I always wait until the last day to enjoy things. I have seen so many things happen at the Dakar, and even more today. I want to stay calm and enjoy things a bit more."
Rodrigues climbed one place to third overall in the standings after his first stage win, but still sits over an hour behind Coma.
Amongst the cars, Spain's Nani Roma got stuck, losing 25 minutes, to allow Mini team-mate Stephane Peterhansel to open up a healthy lead going into the final stage.
Nine-time Dakar winner Peterhansel won Saturday's stage to sit 42mins and 57secs clear of Roma, who has an advantage of more than half an hour over second-placed finisher, Giniel de Villiers in his Toyota.
The finish line is all but in sight, but Peterhansel is keeping things in perspective.
"Victories are earned day by day and I still feel like I am in the race," he said.
"There is still a 30-kilometre special to go and we could have a technical problem. I am still holding my breath this evening. I will breathe again once I am on the podium."
American Robby Gordon saw his hopes all but ended as an aggressive strategy proved costly on the dunes, with the NASCAR star rolling his Hummer and losing 36 minutes.
That leaves him down in fifth place behind another Mini driver, Leonid Novitsky, who finished third.
Tomas Maffei was fastest on the quads but still sits far behind the Patronellis in the overall standings, while Andrey Karginov's stage victory in the trucks did nothing to dent Gerard de Rooy lead of over 53 minutes at the front.
The rally finishes on Sunday in Lima.