Peacock made some history in his big league debut last week in Colorado when he became the first pitcher to debut in an extra-inning game and record a hit and pick up the win since Marino Pieretti with the 1945 Washington Senators.
Smith, meanwhile, made his first big league start Saturday night against the Reds and picked up the win while allowing two runs over six innings.
The 26-year-old has experience pitching out of the bullpen having appeared in six games in relief for the D-backs last year.
"We haven't seen the last of Matt Peacock, that's what I explained to him," D-backs manager Torey Lovullo said. "It's just about going down, keeping the ability to remain stretched out [as a starter] and making sure that he's an option when we need somebody. So that's what we outlined to him."
Asdrúbal Cabrera got the nod there Monday, Wyatt Mathisen started on Tuesday, and Pavin Smith will also get some time.
The right-handed-hitting Mathisen seems likely to play against left-handed starters, while Smith, a left-handed hitter, will get his starts against righties. Cabrera, a switch-hitter, will play there at times, but he is also seeing time at second and third base this year.
"We have really good candidates that can step in there between Asdrúbal , Wyatt and Pavin," Lovullo said. "So we're going to be in good shape there. We feel like somebody is going to be able to step in and give us quality at-bats and play quality defense just like Christian."