Rush completed eight of 11 passes for 46 yards with an interception in Sunday's loss to the Lions.
Dak Prescott got most of the fourth quarter off in a blowout loss, allowing Rush to see his most extensive action of the season so far. The 30-year-old continues to be active ahead of Trey Lance as the Cowboys' No. 2 QB, and Rush would presumably be the pick to move into the starting lineup should anything happen to Prescott.