YG's staying 'bool, balm and bollected' after being detained by police ... mentioning his run-in with cops during his rap battle with The Game ... and brushing it off like it's NBD.

The rapper showed up for a VERZUZ battle Thursday ... only hours after he was detained while law enforcement executed a search warrant tied to a murder investigation ... and he addressed the issue on stage.

YG told The Game ... "I almost didn't make it to this motherf***er" ... a clear reference to his detainment.

The Game told YG he saw the news on TMZ -- we broke the story -- and he worried for his fellow rapper ... and feared their battle might have been scrapped.

As we told you ... YG had a run-in with cops Thursday morning during a SWAT response -- but he was ultimately released.

Cops were executing a search warrant connected to their Drakeo the Ruler murder investigation ... and the property that was searched is connected to YG. He's denied any involvement in Drakeo's murder.

Sources told us VERZUZ was set to go on as planned ... and it looks like the rappers rocked the venue!