King County deputies say the incident unfolded at the Wal-Mart store in Covington at about 8 p.m. Thursday.
According to witnesses, the driver of the SUV appeared to accelerate as the two shoppers were walking through the parking lot area toward the store entrance.
One of the victims, a woman in her 40s, was trapped under the vehicle as horrified shoppers looked on. Passers-by rushed to her aid and were able to free her.
Medics were on the scene almost immediately and rushed the woman and her boyfriend to Harborview Medical Center. The woman suffered injuries to her pelvis and head, and the man sustained head injuries.
"We actually had two deputies that were actually working here overtime for the crowds tonight. They heard loud commotions, saw people running to the area, were immediately able to help the victims and contact the driver," said King County Sheriff's Office spokeswoman Sgt. Cindi West.
Deputies arrested the driver of the SUV, a 71-year-old man, for suspicion of DUI.
He will likely be charged with vehicular assault, West said.