The five-time world champions clawed their way back from 2-0 down to win 3-2 and break Iranian hearts at the Dubai Design District Stadium.
Brazil will meet Italy in the final while Iran will aim for a third-place finish against Belarus on Sunday.
Iran’s Ali Mirshekari gave them the lead with a strike from distance after just 41 seconds.
Just as they did at the start of the tie, the reigning Asian champions got the second period off to a sensational start with Mohammad Masoumi stunning Brazil with a bicycle kick to double the advantage.
Brazil, however, pulled themselves back into the tie through an Allison penalty shortly after.
The South American side upped their tempo with Iran having to work hard to protect their lead but a moment of magic from Allison in the early stages of the third period saw Brazil draw level.
Brazil continued to push and were rewarded with the winner with just 42 seconds remaining on the clock, Brendo's strike taking them within one match of a sixth world title.
MP/TT