The Socceroos were second best for long periods in the Group B fourth-round clash played in temperatures peaking at 35 degrees Celsius.
Oman had been outclassed in losing their opening fixture 3-0 away to Japan on Sunday but Paul Le Guen's side played with much more confidence as they pressured their opponents for large parts of the match.
The hosts had the best chance of the game in the 56th minute, but a brilliant save from Australian goalkeeper Mark Schwarzer turned a diving header from Amad Al Hosni around the post to leave the striker holding his head in his hands.
The opportunity came from a corner, one of several the 97 FIFA-ranked Oman had in the second half as they regularly found themselves in good positions down the flanks against the tiring visitors.
Australia, who lost to Oman 1-0 in Muscat in the third round of qualifiers, had named a defensive starting line-up with forward Harry Kewell up front on his own.
But he, like many of his team mates, struggled in the heat during the match which started with the sun shining bright at 1700 local time (1300GMT), much to the ire of Australia coach Holger Osieck who had questioned the kick-off time.
Both sides were restricted to long shots in a forgettable first period at a half-empty Sultan Qaboos Sports Complex but the second 45 minutes proved more entertaining as space opened up.
Having introduced forwards Archie Thompson and Robbie Kruse off the bench in the second half, Australia produced a late flurry but any winner would have been harsh on the more adventurous Oman.
Thompson, who scored 13 goals in a qualifier against American Samoa in 2001, wasted the visitors' best chance when he miscued an attempted pass with eight minutes remaining when a shot looked the best option.
Australia will be seeking a much improved display in their second match of the group on Tuesday at home to Asian champions Japan, who thrashed Jordan 6-0 earlier on Friday to make it two wins from two.