Five of the injured, including a pregnant woman, were in critical condition, most with head trauma, hospital officials said.
The large SUV was carrying up to 22 people when the driver had tried to circumvent a checkpoint on the highway, Border Patrol spokesman Lloyd Frers said.
With Border Patrol agents in pursuit, the driver attempted to make a U-turn and rolled over, Frers said. He did not know how fast either vehicle was traveling.
"The suburban was grossly overloaded, and it's difficult to handle on that kind of (dirt) road," Frers said.
Sheriff's Maj. Leon Wilmot said the car had swerved to avoid a spike strip put out by Border Patrol agents. Border Patrol spokeswoman Agent Veronica Lozano said she didn't know whether agents put out the device.
Scores of illegal immigrants die each year while crossing the Mexican border into Arizona, many in car crashes. Smugglers often flee from authorities at high speeds or overload vehicles, which makes them difficult to control.
"They just pile in; they're like sardines," Frers said. "It's unfortunate."
Agents are generally required to follow a "non-pursuit" policy, meaning they must follow a suspect vehicle at a distance unless the driver commits a traffic violation, said T.J. Bonner, who heads a union representing Border Patrol agents. After a traffic violation, a supervisor can authorize pursuit.
"Now that you have so many more people making that journey through those godforsaken areas, it's only natural that you're going to have more fatalities," Bonner said.
Four of the injured were at Yuma Regional Medical Center, including one in serious condition, spokeswoman Machele Headington said. The conditions of the others were not known. Three others were treated and released to the custody of Border Patrol, she said.
The Yuma area, a sandy stretch of desert in southwestern Arizona, has become the nation's busiest immigrant-smuggling hotspot. President Bush visited the area in May as part of his push for a sweeping overhaul of immigration laws.
Last month, after a crackdown on illegal border crossing, the Border Patrol's Yuma Sector reported a 48 percent drop in migrant arrests — from 11,522 in June 2005 to 6,030 in June this year.