"I pushed hard on the first stage to gain the advantage, despite the muddy conditions and we found a good pace," said Al Attiyah.
"Now we have a comfortable lead to manage over the coming days. There is a long way to go over many difficult and varied stages," the three-time Dakar champion added.
On the third stage, teams tackle a 243km selective section in a route of 691.35km between Ulan-Ude in Eastern Siberia and the Mongolian capital of Ulaanbaatar (formerly known as Ulan Bator).
Ulaanbaatar is the largest city in Mongolia and is located in the central north of the country in the valley of the Tuul River.
Unlike Al Attiyah, it was a disappointing second stage for the Qatari's two Overdrive Racing team-mates in their Toyota Hiluxes.
Saudi Arabia's Yazeed Al Rajhi and German navigator Dirk von Zitzewitz began the day in third position after a slow puncture cost them a potential second place on the opening day.
But the Riyadh driver suffered technical issues on the special and was not able to continue. The Saudi had been running fastest overall at WP1 (52km) before initially stopping on the track for over 15 minutes and then ceding further time as the stage progressed.
Dutchman Erik van Loon has teamed up with Frenchman Sebastien Delaunay for the first time in Russia, but transmission problems thwarted their progress and they face a fight back through the field over the coming days after losing over two and a half hours to the stage winner after 101km of the stage.
Frenchman Jerome Pelichet had been running second overall after the opening day and he slipped to third with fellow countryman Matthieu Serradori and China's Han Wei following closely in the overall car rankings.