Stave, who took his first career snaps under center last week against Utah State, came in at halftime in relief of starter and Junior Quarterback Danny O'Brien.
"We'll continue with Joel to start," Bielema said Thursday. "We just can't play winning football when we turn the ball over as much as we were.
"He didn't show me any reason not to stay with him."
Stave completed two of his six pass attempts against the Aggies, although two of his passes on third down were dropped.
Stave redshirted all of last season, but did enroll early at the University of Wisconsin in the spring of 2011.