The Mini buggy driver, a two-times winner of the endurance event, had started only 24 seconds clear of Toyota's defending champion Nasser Al Attiyah but extended his lead to 18 minutes and 10 seconds.
The car category's 534km special stage was halted after 223km, with the competitors travelling to the bivouac in liaison.
Frenchman Stephane Peterhansel, a 13-times Dakar winner, was in third place overall and a further 16 seconds behind Al Attiyah.
Two-times Formula One champion Fernando Alonso, Sainz's compatriot, rolled his Toyota on the dunes and continued without a windscreen after losing more than an hour.
He had started the day 10th overall but fell back to 14th.
"It was a dangerous stage with lots of difficult dunes. Several kilometres before the neutralised section, we got completely lost with Nasser and other drivers," said Peterhansel.
"Some drivers got there at the right time, when we eventually found the right way and gained a lot of time. In the end, it’s a good stage for my team-mate Carlos ... whilst we have got a bit closer to Nasser even if we are still in third position."
In the motorcycle category, American Ricky Brabec finished the stage second and extended his lead on a Honda. He now leads Chilean Pablo Quintanilla by 25 minutes.
Australian Toby Price, the defending champion, dropped to fourth overall and 28 minutes off the lead.
The rally, being held in the Middle East for the first time, ends in Qiddiya on Friday. (Reporting by Alan Baldwin in London; editing by Nick Macfie)