Giuliano struck in the 89th minute with the crucial goal that sent the Brazilian side, who won the first leg 1-0 at home in Porto Alegre last week, through on the away goals rule after the tie ended 2-2 on aggregate.
Brazil's Flamengo also won 2-1 away to Universidad de Chile but went out on the away goals rule after their tie finished 4-4 on aggregate after the Chileans secured a surprise 3-2 win at the Maracana in the first leg.
Inter, champions in 2006, go into an all-Brazilian semi-final against three times winners Sao Paulo, who eliminated last year's runners-up Cruzeiro, also of Brazil, on Wednesday.
The match was marred when Inter's reserve goalkeeper Lauro came on after the final whistle and hit Estudiantes defender Leandro Desabato from behind before running into the dressing room as police tried to control the players.
The incident, which seemed to have been sparked by an argument between Desabato and Inter's Argentine goalkeeper Roberto Abbondanzieri, did not develop into a free-for-all.
Estudiantes had taken a quick two-goal lead with two superb strikes in the 19th and 21st minutes.
Captain Juan Sebastian Veron found Leandro Gonzalez with a brilliant, high cross field pass to the left edge of the box where the striker lobbed Abbondanzieri.
Inter had hardly absorbed the shock when winger Enzo Perez cut inside from the left and sent a curling right-footed shot over Abbondanzieri into the top far corner.
As the match approached its end, Estudiantes sat back and allowed Inter to come at them, with disastrous consequences when substitute playmaker Giuliano sent a low shot inside the base of Agustin Orion's far post with one minute to go.
In Santiago, Vagner Love put Flamengo ahead on the stroke of halftime heading in after Adriano's spectacular overhead kick.
The U's Argentine forward Walter Montillo lobbed keeper Bruno for the equaliser in the 73rd minute and Adriano restored Flamengo's lead from Leo Moura's exquisite backheel.
Flamengo's Willians and Vagner Love were sent off in the final minutes, Willians for a second yellow and Vagner Love for dissent.
The Chilean side now meet Guadalajara of Mexico in the semi-finals, which will be played after the World Cup in South Africa ends on July 11.
