The Buenos Aires club, winners of 16 national titles and a record seven Copa Libertadores, will play in Nacional B next season, leaving Boca Juniors as the only Primera Division club never to be relegated.
Angel Correa scored the decisive goal after 60 minutes which earned San Lorenzo the win and condemned Independiente to the drop.
Juan Luis Anangono scored the only goal after 55 minutes as Argentinos Juniors won at home to Colon Santa Fe.
San Martin San Juan were 2-0 winners over Estudiantes with the goals coming from Jorge Luna and Sebastian Penco.
Luna gave the home side the lead after 19 minutes and substitute Penco hit the second with 10 minutes remaining.