Simpson recorded an aggregate time of 2 minutes, 44.895 seconds and recorded the afternoon's fastest lap, blistering around Monterrey's Parque Fundidora road course in just 1 minute, 22.817 seconds while reaching a top speed of 147.2 km/h.
Premat, whose fastest lap of 1 minute, 23.533 seconds, was the second-fastest in the 22-team field will start 0.953 seconds off the lead, followed by Switzerland, Italy and the United States.
"I didn't expect to be on pole when I woke up this morning, the car is working really well and I got to grips with the track quickly," Simpson said, according to a statement posted on the A1 Web site.
"Our progress has been building in the last few races, and my confidence has been building too. There is a great atmosphere in the team and things can only get better."
Friday's practice session featured a wet, slick track and qualifying opened with the course dirty and sticky. Canada's Patrick Carpentier failed to record a time in his second session, after spinning out. His team will begin in 19th place, 4.616 seconds behind Simpson.