Anthony Kiedis Saved a Baby ... DURING Carpool Karaoke!

Anthony Kiedis stumbled into the opportunity to play a real life hero -- for a panicked mom and her unconscious child -- and the rock star knocked it out of the park.

The Red Hot Chili Peppers frontman says it went down while he was shooting that "Carpool Karaoke" with James Corden that everyone's talking about this week.

Anthony described the insane scene when they stopped for a break and suddenly a woman holding a baby ran out of her house screaming, "My baby can't breathe!"

Check out the clip ... AK makes it sound like it was no big deal, but ... IT'S A BIG DEAL!

Witnesses tell us the mom was beyond grateful, and seemingly had NO IDEA a famous singer saved her child's life. Not that it matters.

By the way, Anthony's CPR skills? Honed as a surfer and as a dad.