Argentina are into the semi-finals for the first time in 24 years, despite a richly gifted squad failing to scale the heights expected of it in earlier matches.
They did not exactly set pulses racing at Estadio Nacional on Saturday but were rarely threatened after Gonzalo Higuain's well-taken opener in the eighth minute.
The Netherlands or surprise package Costa Rica will face Sabella's men in Wednesday's last-four clash in Belo Horizonte.
"It is a great joy for all," the manager told reporters. "It was [our] best match of the World Cup."
"Netherlands or Costa Rica? God will say."
Higuain almost added a spectacular second after half-time and the Napoli forward was left to reflect on a return to form after appearing off the pace in previously in Brazil.
"This group deserves this," he told reporters.
"I could see that the ball was coming my way, and I managed to hit it sweetly at the most important moment.
"Now we are in to the semi-final, but we have to aim for the final."
After the match, full-back Pablo Zabaleta tweeted: "The dream of this group and of the 40 million Argentines is still alive!!"
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