Which civil rights tactic was most directly responsible for african americans' gaining equal access to the ballot box, especially in southern states, during the 20th century?

Non-violent protest--blacks participating in the marches and non-violent protests eventually gained attention and led to the Voting Act and Civil Rights Act. 

As blacks continued non-violent protest but were met with violence the media exposed the actions revealing to the whole country. LBJ could not longer ignore the concerns of blacks in the country and encouraged the passing of the Voting Rights Act (1965) and the Civil Rights Act (1964).