Jesus Christ is the only one who can cleanse us of our sins. He took our sins to the cross, and died because of them. By our faith in His atoning death, we can be saved, because His blood was shed for the specific purpose of washing away our sins. Note the sequence in the above verse. Believe and be baptized and you will be saved.
Belief comes first, and then baptism.
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost. The act of baptism is not magical, and does not by itself cleanse anyone of sins. That is not what these verses mean. A confessed faith in the atoning death and resurrection of Jesus Christ is what really saves. John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.