The Persians emerged victorious over their European rival in penalty shootout 5-4 after the match ended in a 5-5 draw.
Iran will play winner of Austria and Argentina in the semifinals on Saturday.
Iran was defeated against Argentina 5-4 in Pool B in its opening match and defeated the US 8-3 and Australia 6-4 in its following matches.
Team Melli was also held against South Africa (4-4) and Czech Republic (8-8), respectively.
The competition started in Pretoria on February 5 and will run until February 11.