Spalletti took over following the sudden resignation of Roberto Mancini last month and inherited a side which had already lost to England in their opening fixture.
Ciro Immobile broke the deadlock two minutes into the second half when he headed in a rebound after Nicolo Barella’s volley struck the crossbar.
North Macedonia - who beat Italy in the 2022 World Cup play-offs - got back on level terms with nine minutes left through a fine free-kick from captain Enis Bardhi.
The draw left Italy third in the group, having played three games.
AAP