Star striker Lionel Messi will miss the country's three remaining qualifying matches due to suspension.
Argentina have qualified for every World Cup Finals since 1970.
"I am grateful to the players because they are responsible for this option that Argentina can go to the World Cup", Bauza said.
The 59-year-old has been relieved of his duties, with the Albiceleste precariously sitting fifth in CONMEBOL World Cup qualifying.
The Argentine Football Association have announced the sacking of worldwide team manager Edgardo Bauza.
The fifth-ranked side will advance to a playoff against the top nation from Oceania.
The top four in the 10-nation group go through to the 2018 finals in Russian Federation, while the fifth-placed country qualifies for a playoff against the Oceania top qualifier, which could well be New Zealand.
Bauza was appointed manager after his remarkable spells as club coach with Ecuador's LDU Quito and Argentina's San Lorenzo.
The likes of Atletico Madrid's Diego Simeone and Sevilla's Jorge Sampaoli have both been linked with managing their country, yet it's hard to see either of those bosses leaving their respective clubs.
Bauza's replacement faces the no small task of a friendly against Brazil - who have already booked their place at the World Cup - in Melbourne on June 9.
Argentina just beat Chile 1-0 in qualifying last month before falling 2-0 at Bolivia days later.
The Argentine Football Association confirmed Monday that Bauza's reign was over after just eight matches in charge.
Bauza, who succeeded former Barcelona coach Tata Martino back in August, endured a torrid time as manager with a 3-0 loss to Brazil the pinnacle of his failures.
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