RCMP say a 21-year-old woman was in hospital Tuesday in serious but stable condition, and two men, aged 20 and 24, and a 20-year-old woman, died at the scene.
They say no names will be released.
The SUV was heading south on Highway 2 on the south side of the city when it went out of control Monday morning.
Insp. Gibson Glavin said it's believed the vehicle veered onto the shoulder of the road over some rumble strips, then it appeared as if the vehicle took a sudden jerk away, as if someone was trying to correct the vehicle's direction, before it rolled several times.
University of Alberta president Indira (in-DEER'-ah) Samarasekera (SAM'-rah-SAKE'-rah) says two of the dead were students and the other was a former student.
"Words seem inadequate to express the sadness enveloping our campus today," she said in a statement posted Tuesday on the university's website.
"Two of our students and a former student lost their lives in a tragic car accident yesterday and a fourth person is in serious condition in hospital. On behalf of our university community, I wish to send my heartfelt condolences to the families and friends of the students who died. Our prayers are with the survivor."
Samarasekera also urged students or staff who have been affected by the deaths to reach out to several supports offered on campus.
"This is a sad day for the University of Alberta, and most especially for the families and those closest to these young people. I know that our supportive community will come together and that our caring thoughts will, over time, bring some small measure of peace to those who have lost loved ones this weekend."
RCMP also say its victim support services are in place to assist family and friends of the victims.
Police continue to investigate.