Iran captain Milad Ebadipour and Morteza Sharifi earned 18 points each and Amin Esmaeilnezhad also had 17 points for Team Melli.
Issa Mohamed Moustafa had 16 points for Egypt in the match, held at Arena Stozice in Ljubljana, Slovenia.
Iran will play group leader Netherlands on Wednesday.
Behrouz Ataei’s men started the campaign with a 3-2 win over Argentina in their opening match.
The competition has brought 24 competing teams in six pools of four, playing in a single round-robin format from Aug. 26 to Sept. 11.
The top two teams in each pool and the four best third-placed teams will qualify for the elimination round.