No, I do not believe it is baptism that saves us. The thief on the cross was never baptized and yet Jesus told him “this day thou shalt be with me in Paradise.”
But my point was the NIV left out the eunuchs confession of Jesus. Romans 10:9-10 reminds us that it is “with the mouth that confession is made unto salvation.”
Without that confession it would not have mattered if the eunuch was baptized or not. Without confession of Jesus he would not have been changed and made new on the inside. And yes, I do believe that it takes the shed blood of Jesus to redeem us. But Jesus also said that if we deny Him, He would deny us.