Patricia Mendez, 62, and eight-year-old Ava Lucia McWhirter died at the scene.
The driver of the other vehicle, 51-year-old Jeffrey Howard of Wolfforth, was flown by helicopter to University Medical Center in Lubbock.
He was in satisfactory condition after the wreck.
The accident occurred shortly after 9 a.m. on U.S. Highway 84, about a mile east of Anton.
The Shallowater Police Department received a 911 phone call about a vehicle headed west at a high rate of speed on the wrong side of U.S. Highway 84.