"It was a great stage for us. We only had a small puncture, which only cost us two minutes," said Al Attiyah.
"It's a good day, we have reason to be happy. From what I've heard, there's going to be lots of fesh-fesh tomorrow, we'll have to keep our guard up in the marathon stage. After that, we'll keep attacking," added Al Attiyah, who has Frenchman Mathieu Baumel as his navigator.
75th career stage win
Peterhansel is third overall, 7min 03sec off the lead, after claiming his 75th career stage win on the race.
"It was a nice stage, with tough dunes and tricky navigation: hard-to-find waypoints in the valleys. It was a quintessentially Peruvian stage and the sign of things to come in the next few days," said Peterhansel.
Meanwhile, Sebastien Loeb's dream of adding victory in the gruelling endurance race to his nine world rally titles suffered a fog-hit setback.
Loeb, driving a private Peugeot and who won the second stage, was 42 minutes behind Peterhansel after a difficult day in which he lost his way in the fog and is eighth overall.
Nightmare for Sainz
Defending champion Carlos Sainz, like Loeb a former world rally champion, suffered a nightmare third stage when the front suspension on his Mini broke in the early stages of the run.
The Spaniard was held up for over three hours as a result, sending him down the standings.