The Cowboys punted on their first drive. Dak Prescott threw an interception on their second.
The third time was the charm as Dallas drove 65 yards in 11 plays to take a 7-3 lead on the 49ers.
Ezekiel Elliott ran it in from the 1-yard line after a defensive pass interference penalty on Charvarius Ward moved the ball from the 10 to the 1 on a pass intended for Luke Schoonmaker.
Rookie center Cooper Beebe saved the drive for the Cowboys after KaVontae Turpin fumbled on an 11-yard gain on third-and-9 from the Dallas 36. Beebe fell on the loose ball.
Prescott is 8-of-9 for 62 yards, with CeeDee Lamb catching five for 40 yards.
Running back Dalvin Cook has made his Cowboys debut, rushing three times for 7 yards.
