Chiefs Legend Neil Smith: Play-By-Play of Pregnant Woman Flood Rescue

Chiefs legend Neil Smith rescued a pregnant woman stuck in a severe flood earlier this week ... and now he's walking us through the harrowing experience.

Smith -- who played 13 seasons in the NFL, made 6 Pro Bowls and won 2 Super Bowls -- saw a woman trapped in her car on Tuesday on a severely flooded street near his home in Lee's Summit, Missouri.

FYI -- the area has been pounded with a historic amount of rain.

The 6'5" ex-NFL star tells us he immediately jumped into action (after he took off his shoes) and made a beeline for the woman ... reaching her and escorting her to safety, unhurt.

"Everything I've ever done, both on the field and in life, I just react to things. Fortunately I was just there for her at a good time," Smith says.

"Thank God I was there at the right time to try and help her out, where life can just go on for another day."

Incredible story.