Holger Osieck's men could not find a way past the hosts and had to be thankful to goalkeeper Mark Schwarzer for keeping a clean sheet
After chief rivals Japan thrashed Jordan 6-0 earlier in the day to lead Group B with six points, the Socceroos were keen to make a strong start to their own campaign, prior to a vital clash against the Blue Samurai in Brisbane on Tuesday.
Head coach Holger Osieck made three changes to his side which suffered a 2-0 defeat in Copenhagen last Saturday.
Matthew Spiranovic, Mile Jedinak and Archie Thompson all made way for Sasa Ognenovski, Carl Valeri and David Carney.
In a first half that lacked any rhythm, it was Oman who settled the quickest during early proceedings, with Australia struggling to adapt to the oppressive conditions of around 40 degrees at the Sultan Qaboos Sport Complex.
But despite drawing two fouls in dangerous positions during the opening 10 minutes, the hosts failed to create any clear-cut chances.
As the half wore on, the Socceroos began to hit their stride, and Carney registered Australia's first shot on target after 20 minutes.
The Bunyodkor full-back unleashed a fierce strike from outside the box, only for Oman goalkeeper Ali Al-Habsi to tip the ball away for a corner.
Mark Bresciano and Valeri started to enjoy more time on the ball and the latter had two opportunities to give Australia the lead in the space of three minutes.
But Al-Habsi was up to the task, denying the Sassuolo midfielder on both occasions.
Valeri tested the Wigan Athletic shot-stopper from distance on 32 minutes, only to have his strike tipped away for a corner.
And three minutes later the 27-year-old had a low shot pushed away following some strong work from Harry Kewell inside the penalty area.
Oman held the advantage in the second half, forcing Australia deep into their defensive half for prolonged periods of time, and the hosts' dominance was almost rewarded courtesy of Amad Al Hosni.
The striker's 57th-minute header seemed destined for goal, but Australia goalkeeper Mark Schwarzer's remarkable save ensured the scores remained level.
Osieck's side rarely threatened and struggled to cope with the conditions, although they had a chance to snatch all three points on 82 minutes.
Lively substitute Archie Thompson found himself one-on-one with Al-Habsi but he failed to score from inside the six-yard-box, after appearing to be crossing to Bresciano rather than shooting.
Paul Le Guen's men were full value for their point and the Socceroos now return to Australia with plenty of work to do ahead of Tuesday's clash against table-topping Japan at Suncorp Stadium.