Sainz, father of the Formula One driver of the same name, won the 425km timed section of the 727km seventh stage from La Paz to Uyuni to lead Toyota’s Qatari driver Nasser al-Attiyah by an hour and 11 minutes.
Peterhansel, who had been 27 minutes ahead of Sainz after leading the rally from Peru into Bolivia, hit trouble while trying to overtake a motorbike at the 186km mark and came to a halt.
The Peugeot’s left rear wheel, upper suspension link, shock absorber and radiator were all damaged.
The Frenchman was helped back on the road by compatriot and team mate Cyril Despres, the five-times Dakar winner who had long dropped out of contention for the overall victory.
Peterhansel ended the stage third overall, an hour and 20 minutes off the lead.
Peugeot, who are pulling out of the South American event after this year, will now be hoping 2010 Dakar winner and two-times world rally champion Sainz keeps out of trouble in motorsport’s most gruelling endurance test.
In the motorcycle category, French Yamaha rider Adrien van Beveren reclaimed the overall lead from Argentina’s Kevin Benavides, on a Honda.
Van Beveren was three minutes and 14 seconds clear of his rival.
Sunday sees the longest special stage of the rally, a 498km timed section from Uyuni to Tupiza that includes high-altitude sand dunes at 3,500 meters.
The rally finishes in Cordoba, Argentina, on Jan. 20.
Reporting by Alan Baldwin, editing by Pritha Sarkar