Danilo gave Brazil a 1-0 lead in the 12th minute with a header from a corner, but Egypt equalized through Omar Gaber in the 26th.
Egypt deserved at least a draw, as it was sharper in attack, tougher in defense and always able to keep Brazil on edge with its counterattack.
Brazil and Egypt each have one point in Group E, the same as Austria and Panama, who drew 0-0 in a match earlier Friday.
Gaber equalized in the 26th, scoring from 10 meters (yards) after Danilo failed to clear a cross into the area. The low shot got through the hands of Brazil goalkeeper Gabriel.
Gaber could have given Egypt at 2-1 lead in the 48th, but despite taking his time and being left along he shot just wide of the far post from 12 meters (yards).
In the 85th, Egypt goalkeeper Ahmed Elshenawi had to leave the match after being struck in the face by Henrique, who chased a loose ball into the area and inadvertently kicked Elshenawi in the face. Egypt had a substitution up its sleeve to allow the back-up keeper to come on.
The performance has to make Egypt one of the early dark-horse choices for the title while casting doubt upon the claims of Brazil, which is a perennial favorite in any tournament.
Brazil faces Austria next and Egypt goes against Panama.