Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord. (Romans 5:20-21)
The law cannot save us. In fact, Paul teaches us that it even increases our guilt before God. But the life, death and resurrection of the Lord Jesus Christ caused such a radical and permanent change in human history that, where sin used to increase and dominate, God's grace is now superabounding and surpasses sin.