Duffy took over from Kenny Shiels as Greenock Morton manager on 19 May 2014. He signed a two-year contract with the club. His first match was a 1–0 home win over Spartans in the Scottish Challenge Cup on 26 July 2014. Three wins and a defeat in the league saw Duffy awarded manager of the month in League One for November 2014. His Morton team, however, did suffer a shocker in the Scottish Cup at the hands of Spartans in a 2–1 defeat in November, a Spartans team that had knocked out his former club Clyde in the previous round. He eventually led the Ton to the Scottish League One title which was clinched on the final day in a closely fought contest in the 2014–15 season, his first silverware as a manager. After leading Forfar Athletic on goal difference going into the last game, Morton recovered from 1–0 down against Peterhead to win 3–1 at home on the last day to win the title by three points and clinch automatic promotion to the Scottish Championship.