"I'm very grateful to the players," the 52-year-old told reporters after Wednesday's victory in Doha. "They all stood up."
Okada had acknowledged that anything less than victory could result in his dismissal after last month's 1-1 home draw with Uzbekistan triggered widespread criticism.
The three-times Asian champions are second in Group A with seven points from three games. Leaders Australia have a maximum nine points after winning 1-0 in Bahrain.
Celtic midfielder Shunsuke Nakamura, who played with a heavily bandaged left knee, orchestrated Japan's win with Tatsuya Tanaka, Keiji Tamada and Brazilian-born defender Tulio scoring the goals.
"We expected a tough game but the players didn't flinch or try and hide," said Okada, who led Japan to their first World Cup finals in 1998 during his first spell in charge.
"They showed what they were made of. We fixed the mistakes we made against Uzbekistan and we passed and moved very well. I'm very satisfied."
Former Japan coach Ivica Osim had done little to ease the pressure on Okada in the run-up to the game by saying failure to qualify for the World Cup would be a national disgrace.
"You wonder what will happen to Japanese football if they don't qualify," said the Bosnian. "Players like David Beckham and Roberto Carlos deal with pressure every day.
"Japan's players need to think about what would happen if they fail. If they read the newspapers and feel nothing about it then they should quit."
Qatar remained third with four points from four matches. The top two from each of the two five-team groups qualify automatically for the 2010 finals in South Africa.
