Liverpool's No.9 was introduced 12 minutes from time at the Rostov Arena as Selecao coach Tite sought a late winner after Steven Zuber had equalised Philippe Coutinho's opener.
Firmino's first involvement saw him send a half-volley off-target from a tight angle, and he then forced Yann Sommer into a save from a header in the 90th minute.
But Switzerland successfully resisted late Brazilian pressure to earn a point in their opening Group E fixture.