Striker Martin Palermo scored two minutes into stoppage time in torrential rain giving Argentina a 2-1 win and reviving hopes of qualifying for the 2010 finals.
They have climbed into fourth place in the South American group before their last qualifier away to Uruguay on Wednesday.
An emotional Maradona celebrated his team's first victory after three consecutive losses with a belly-flop on the rain- soaked field. Later he told reporters a miracle by 'Saint Palermo' had granted the team another life.
They say Maradona's deficiencies as a coach have placed top players too close to failure in what could be Argentina's first elimination from the finals since 1970.
"Maradona is the greatest idol of Argentine soccer but if you ask people, 50 percent of them, including me, will tell you that he shouldn't be the coach," Carlos Andrade, a Buenos Aires taxi driver, said.
"He doesn't have the experience. It's something we tend to do in Argentina - from the president to the national coach - everyone improvises."
Even before he took the job sceptics queried his limited coaching experience and questions linger after Saturday about Maradona's lack of strategy.
"I want Argentina to reach the World Cup and win it but they have to change the way they're playing," said Maximiliano Reynosa, a pizza deliveryman.
"No one denies Maradona is one of the best players but he's a mediocre coach. We're relying on a last-minute goal from (Palermo) a 35-year-old player."
"Maradona is the best. He's a God," said Florencia Sassani, a 21-year-old college student, wearing a light blue Argentina jumper. "He's had some back luck in the past but he won today and he'll do well, God willing."
