Frenchman Peterhansel began the day in the overall lead following his victory in Monday’s second stage, but punctured six times as he came home in 28th place, more than 28 minutes down on Roma.
Poland’s Krzysztof Holowczyc came in second 1min 07sec down with South African Leroy Poulter third at 3min 19sec.
In the overall standings, Roma leads a trio of Mini drivers with Argentine Orlando Terranova second at 9min 06sec and Nasser Al-Attiyah of Qatar in third at 10min.
Terranova was fourth on the day, losing just under 5min to Roma while Al-Attiyah came in seventh after suffering four punctures, and lost just over 10min.
Peterhansel is down in fifth place overall but is 24min 08sec behind Roma.
And the 11-time former winner (six times in the moto section and five times in cars) admitted he had not enjoyed the 301km timed section from San Rafael to San Juan.
“I’ve never known a Dakar stage like this one,” said a frustrated Peterhansel.
“It was a nightmare today. We punctured six times! Unfortunately we opened on the course and we paid for it.
“On the first I hit a big rock, that’s my fault, but then we were the first to go out and we found ourselves completely off-piste in very tall vegetation thanks to a last-gasp swerve due to bad weather and mud.
“And when we got out of that, we had three slow punctures out of four wheels, certainly due to the pines in the sides of the wheels.
“Unfortunately, as we were the first car, we cleared the track for the rest behind. We were thrown into the lion’s den but I can’t see how we could have done anything differently.
“We couldn’t have imagined that in clearing a path in the vegetation we’d get three punctures out of four.”
For Roma it was a particularly satisfying day.
“You know, sometimes the Dakar is crazy and this stage was like that,” he said.
“The drivers in front of me had some problems and I tried to be really concentrated all through the stage and not make mistakes.
“Anyway, I’ve got here and I’m happy, but on the Dakar, Valparaiso is still far. We need to be like that and really concentrate every day.”
In the motorcycle section, Spaniard Joan Barreda on a Honda increased his overall lead by winning the third stage, a 373km timed special.
Frenchman Cyril Despres on a Yamaha came in second 4min 41sec back with Spain’s Marc Coma third on a KTM at 6min 56sec.
Those three remain in those exact positions in the overall standings with Barreda holding a lead of over 13 minutes.
It was a particularly physically demanding course for the motorcyclists despite the length of the stage being reduced due to heavy rain.
At one point they reached 4.3km above sea level.
It proved treacherous for one rider as Portugal’s Ruben Faria had to be air-lifted to hospital by helicopter after a crash, although that was more for precautionary reasons than anything else.