It's not necessarily that the 13th Amendment overturned the Dred Scott Supreme Court decision, it's that it outlawed slavery in the United States, meaning it granted to right of liberty to all Americans.
The Supreme Curt decision Dred Scott was proclaimed on March, 1857. It established that slaves did not have the right to access justice since they were not considered citizens of the United States. The Dred Scott decision was overturned by the 13th Amendment to the Constitution. This Amendment established the citizenship of all person and ended slavery. So it granted freedom and citizenship to people of all races and creeds.