The Australian rider finished second as stage 11 was halted prematurely with Price just 18 seconds behind Frenchman Antoine Meo.
The strong ride in stifling heat allowed him to add a further 12 minutes to his overall margin over Stefan Svitko and he now leads the race by 35 minutes and 23 seconds.
“I can’t smell victory yet, not yet,” Price said.
“I won’t smell victory until I cross the finishing line on the last day.
“We’re another day closer, but for sure, it’s been a hard one.”
The 28-year-old from Singleton in New South Wales’ Hunter region said he struggled to get airflow as the mercury soared in the last 50 to 80 kilometres.
“It’s been hard on the bikes today. There’s been a lot of hot weather,” Price said.
“The bike is still going really well, there’s no water leaking or anything.
“It still feels strong, so we’re in a good spot.”
“We’ve made a bit of time on the overall second placed rider which is our main goal and hopefully the next two days we can take it a little bit easier,” Price said.
Former race leader Paulo Goncalves crashed out of the rally after a fall early in the day.
Price, in his second Dakar, will now turn his attention to the 481-kilometre penultimate stage through semi-mountainous regions from San Juan to Villa Carlos Paz.
In the car division, Stephane Peterhansel leads by more than 50 minutes despite finishing fourth behind Qatar’s Nasser Al-Attiyah on stage 11.