The visitors appeared to be in trouble when midfielder Pablo Guinazu was sent off after only 24 minutes of the match in La Plata.
But 10 minutes later, the Argentines gave away a penalty when Leandro Desabato fouled Nilmar and Alex Meschini converted for the only goal of the match.
Estudiantes, with former Lazio and Manchester United midfielder Juan Sebastian Veron orchestrating midfield, dominated the second half, repeatedly pumping high balls into the area.
But Internacional defended superbly and were rarely threatened, repelling everything the hosts threw at them.
"It was a strange game, I can't really describe it," said Veron.
The second leg will be played in Porto Alegre on December 3.
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