La Liga's reigning champions have now drawn two and won three of their opening five games.
The veteran striker went on as a 71st-minute substitute with Rayo 1-0 ahead.
Barcelona have made a solid start in La Liga and for now, the hope is an upturn will postpone bigger, and more expensive, decisions until later.
Barca said both players are "unavailable for selection" and their "return will depend on the recovery".
Griezmann was replaced in the 58th by João Felix, who hadn't played this season because of an injury.
La Liga president Javier Tebas delivered some familiar broadsides on Sept 7 about PSG benefiting from state funding, followed by fresh digs against the club for signing Lionel Messi from Barcelona.
Fernando Morientes, who has worn the jersey of Barcelona's eternal rivals Real Madrid, is in admiration of the gesture made by players like Gerard Piqué, Sergio Busquets and Jordi Alba
The Colombian's last club was Turkey’s Galatasaray where he played from 2019 until the end of last season.
Most would describe an unbelievable transfer window as one in which both Messi and Ronaldo change clubs. Well, that's exactly what happened. And there were many more unexpected moves across leagues.
Lamela got the winner from inside the area by picking up the rebound from Rafa Mir's shot that hit the post after a breakaway three minutes into injury time.
A look at what’s happening in European football on Saturday.
The French striker finally has the opportunity to take centre stage and become a protagonist in Messi’s absence.
The big point of interest over the weekend was whether FC Barcelona will be able to cope in life minus Lionel Messi.
Manchester City begins the defense of its Premier League title with a trip to Tottenham, for whom the champions' transfer target Harry Kane could feature.
The Catalan club will have to find a way to succeed without Messi, while still facing the difficult financial situation that led to his departure.