The Reds became the first Brazilian team to win the trophy, the region's equivalent of the UEFA Cup, in its six-year history despite being outplayed at home from much of the second leg.
Leading 1-0 from last week's first leg away from home, Internacional fell behind when Agustin Alayes scored for the Argentines midway through the second half before Nilmar scrambled the equaliser in the 115th minute.
A foul-ridden first half produced only a couple of moments of excitement.
Estudiantes forward Mauro Boselli had a goal harshly ruled out for offside midway through and Internacional midfielder Andrezinho forced a superb one-handed save from Mariano Andujar just before the break.
Apparently happy to sit on their lead, Internacional handed Estudiantes the initiative and paid the price in the 65th minute when Leandro Benitez floated over a free kick from the left and Alayes, unmarked at the far post, volleyed in.
Boselli missed his kick after a flowing move and Marcos Angeleri fired narrowly wide in the 90th minute as Estudiantes came close to settling the tie in 90 minutes.
Internacional took control after Estudiantes captain Juan Sebastian Veron hobbled off injured in extra time.
Estudiantes survived a goalmouth scramble with Andujar brilliantly saving at point-blank range from Bolivar in the first half of extra time and Marcos Angeleri headed a dangerous cross out from under his crossbar.
The pressure paid off when Internacional won a corner, Bolivar headed against the bar and Nilmar scrambled the ball home with five minutes left for his fifth goal of the tournament.
Estudiantes's frustration boiled over when Rodrigo Brana and Boselli were sent off in the last three minutes, the latter for kicking Andres D'Alessandro. (Writing by Brian Homewood in Buenos Aires; Editing by Peter Rutherford)
