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The Azzurri host Andy Farrell's side on Saturday in their third match, looking to avoid a record-extending 30th consecutive defeat in the tournament going back to 2015.
Italy lost 41-18 to England last time out after the team also fell 50-10 to France in Rome.
"We've worked a lot on ourselves focusing on our game plan," Smith said. "Against Ireland we aim to show the same attitude as in the last match with the aim of taking another step forward."
Wing Monty Ioane earns his fourth cap after scoring his first Italy try against England, in an enlarged triangle alongside Jacopo Trulla and Luca Sperandio.
Centre Carlo Canna, Italy's most experienced player, earns his 50th cap, playing alongside Juan Ignacio Brex, who gets his third call-up having made his international debut in the opener against France.
Flanker Michele Lamaro, in doubt after an ankle knock against England, holds his position but Danilo Fischetti, who was hit on his shoulder in the same match, will not feature.
Fly-half Tommaso Allan, who came off the bench to scored a try and a conversion against England, has also been ruled out after taking a knock to his ribs playing for club side Treviso.
On the bench, Zebre wing Mattia Bellini makes the Six Nations list for the first time this season, with flanker Maxime Mbanda and prop Cherif Traore also replacements.
The match will be the 33rd between the two nations, with Italy beating the Irish just four times, most recently in the Six Nations in March 2013 in Rome.
Ireland has lost its opening two games, against Wales 21-16 and France 15-13.
Italy team to play Ireland in the Six Nations at the Stadio Olimpico in Rome:
Jacopo Trulla; Luca Sperandio, Juan Ignacio Brex, Carlo Canna, Monty Ioane; Paolo Garbisi, Stephen Varney; Michele Lamaro, Johan Meyer, Sebastian Negri; David Sisi, Marco Lazzaroni; Marco Riccioni, Luca Bigi (capt), Andrea Lovotti
Replacements: Gianmarco Lucchesi, Cherif Traore, Giosue Zilocchi, Niccolo Cannone, Maxime Mbanda, Callum Braley, Federico Mori, Mattia Bellini
Coach: Franco Smith (RSA)