I would like to share a few verses and some comments that I hope will answer this question for you. The thief on the cross admitted that he had sinned and put his faith in Jesus to save him. He was not baptized, yet Jesus told the thief that he would be with Him in paradise that day.
Luke 23:41-43 And we indeed justly; for we receive the due reward of our deeds: but this man (Jesus) hath done nothing amiss. And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily, I say unto thee, Today shalt thou be with me in paradise.
Baptism is a symbol of our death, burial & resurrection with Christ. Going down into the water symbolizes our death to sin (that Christ has taken away our sins) & coming up out of the water symbolizes our new life (that we should live for Christ in this life as well as having eternal life to look forward to).
Romans 6:3-6 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection: Knowing this, that our old man is crucified with him, that the body of sin might be destroyed that henceforth we should not serve sin.
Baptism is an outward showing of our faith in Christ and it pleases Him for us to be baptized. However, baptism is not what saves us. It is important to remember that it is faith in Christ & asking Him for forgiveness that saves us. There is not anything that we can do to save ourselves.
1 Peter 3:21 The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ.
Eph. 2:8, 9 For by grace are ye saved though faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.
God makes it clear in His Word that to be saved we have to put our faith In His Son, Jesus, for our forgiveness and salvation. Nothing else can save us. Jesus says in John 14:6 I am the way, the truth, and the life: no man cometh unto the Father, but by me.