Despres ended the day with a 27-second lead over his compatriot, team mate and defending champion Stephane Peterhansel, who is chasing his 14th Dakar title.
Peugeot finished one-two-three in the stage, with nine-times world rally champion Sebastian Loeb third after losing his brakes on Saturday.
South African Giniel de Villiers was in third place overall for Toyota, however, five minutes 44 seconds behind Despres.
Toyota's Al-Attiyah had the handicap of opening the 267-km stage, a loop around Pisco, with no motorcycle tracks for guidance this time and his French co-driver Matthieu Baumel feeling unwell in a stage requiring careful navigation.
The Qatari dropped to fifth overall, 12 minutes 15 seconds off the lead.
"It was not easy, Matthieu was completely sick after 15km and we needed to take care," said the two-times winner.
"We are quite happy to finish... tomorrow we'll have a better road. If we start in a good position, it will be no problem, I think."
In the motorcycle category, Britain's defending champion Sam Sunderland lost the lead to Honda's Spanish rider Joan Barreda and fell to fourth overall.
Barreda leads French Yamaha rider Adrien van Beveren by two-and-a-half minutes.
Monday's 296-km third stage is south from Pisco to the coastal town of San Juan de Marcona.
(Reporting by Alan Baldwin in London, editing by Clare Fallon)
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