The team from the northern suburbs of Buenos Aires, who are in their first even continental competition, bounced back from the 1-0 defeat suffered in Asuncion with a thrilling second leg.
They established a three-goal advantage in the first 50 minutes courtesy of goals by defender Mariano Echeverria, young star Ruben Botta and forward Federico Santander.
But that work was undone for Nestor Gorosito's team in only nine minutes: a header by Santiago Salcedo and a precise free-kick by Jonathan Fabbro made it 3-2, which would have put Cerro Porteno through.
Defender Alejandro Donatti became Tigre's saviour when he prodded home a Norberto Paparatto header. In the last 10 minutes, Botta saw red but his team held on.
"This triumph gave us a great happiness," said coach Gorosito.
On man-of-the-match Botta he added: "Ruben is very young and he still isn't playing his best. I'm sure that a European club will offer millions for him soon."
Now, Tigre will face in semi-finals the winners of the tie between Brazil's Gremio and Millonarios of Colombia.
But, the 'Matadores' qualify for the next Copa Libertadores as the best Argentinian team in this Copa Sudamericana as Independiente lost 2-1 to Universidad Catolica in Santiago.
After the first leg finished 2-2 in Avellaneda, the Chileans took a quick advantage in the second match with a penalty by Michael Rios.
Jonathan Santana's 35th-minute strike gave some hope to the team coached by Americo Gallego, but only three minutes later Rios, with another penalty, made it 2-1 for a 4-3 aggregate win.
Universidad now face Brazilian giants Sao Paulo.