Kobe Bryant Rushes to Lamar Odom's Bedside ... Prays with Kardashians

Kobe Bryant left a Lakers pre-season game in Las Vegas early ... and rushed to the bedside of his former teammate Lamar Odom Tuesday night -- where he prayed with members of the Kardashian family.

Bryant and the Lakers happened to be in Vegas to play the Sacramento Kings -- but when Kobe got word about his friend, he left the MGM Garden Arena and beelined it for the hospital.

Lakers general manager Mitch Kupchak was also at the hospital with Kobe.

As we previously reported, Khloe, Kim and Kris Jenner had also rushed to the hospital to be with Lamar -- and when Kobe arrived, they all prayed together.

We're told as of this morning, Odom's condition is essentially the same ... he's in a coma and his heart is failing, but he's still alive.