Boxberger, who joined the team May 2, allowed one unearned run in two appearances that covered 3 2/3 innings. He pitched 1 1/3 innings in relief in Friday's 6-3 loss to the Rays at Tropicana Field.
San Diego manager Bud Black made note of Boxberger's performance and the way he handled himself during his stint on the roster. This was the fifth time Boxberger had been added to the Major League roster in the last two seasons and the first this season.
"Major League success or performance that is sustained happens for guys at different timelines," Black said. "Last night, when we told him he was going to Tucson, we told him that his two outings here and how he carried himself was better than any time that we've seen him. He looked like a Major League pitcher."
To make room for Smith on the 40-man roster, the team designated right-handed pitcher Fautino De Los Santos for assignment. Santos was 0-1 with a 3.86 ERA in two games for Tucson in the first week of April.
The Padres claimed De Los Santos off waivers from the Brewers on Feb. 6. He was optioned to Tucson on March 12, after he allowed three runs in four innings during Spring Training.
Smith, the Padres' No. 20 prospect, joined the team Friday after posting a 1.15 ERA in six starts for Double-A San Antonio. A 14th-round Draft pick only two years ago out of the University of Oklahoma, Smith has moved quickly through the system.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.