Portuguese Jose Peseiro, who took over five weeks ago with the Saudis staring at early elimination, believes the late fightbacks in their last two qualifying wins were no fluke and a top-two finish is a realistic goal.
The Saudis are currently level in Group Two with second-placed North Korea on 10 points, one behind 2002 World Cup semi-finalists South Korea, who have played one less game.
"It will be difficult but we aim to win all our games and if we do that, we will go through automatically," Peseiro told Reuters by telephone.
"This is football, we have seen that anything can happen, so why can't we do this?
"We have the ability, the motivation, the confidence and a little luck too," added Peseiro, who became the Saudi's 20th coach in the last 15 years.
The Gulf giants came back from a goal down late in Wednesday's game to beat United Arab Emirates 3-2 and thrust their way into contention for a place at their fifth-successive World Cup.
The former Sporting Lisbon and Panathinaikos boss also said former Asian player of the year Yasser al-Qahtani, who he sensationally dropped for Wednesday's game, would have to fight to get his place back.
"Al-Qahtani is a great player but he didn't show up for training or answer my phone calls," Peseiro said.
"I cannot accept this from any of my team. We have 26 players and he will have to earn his place."
