Japan inflicted group leader Saudi Arabia's first defeat of the campaign earlier on Tuesday in Saitama.
It means Australia have to beat the Samurai Blue in Sydney on March 24 to have any hope of securing one of the two automatic qualifying spots.
"Very disappointing. We came here, we prepared well and at the end of the day it's not good enough to take something away from the game," Socceroos captain Mat Ryan told Network 10.
"It's not the first time it's happened this campaign so it's very disappointing on that aspect."
Australia went into the match without Riley McGree after the attacking midfielder tested positive to COVID-19, but made a near-perfect start.
The Scottish-born winger brought down a Jackson Irvine ball brilliantly before being felled by the Omani goalkeeper with Maclaren stepping up for his second goal in a week for the national team.
Oman, who were missing several players due to a COVID-19 outbreak in their squad, came out firing in the second-half and equalised in the 54th minute through a stunning strike from Fawaz.
The midfielder had time on the edge of the box to fire a right-foot stunner into the top corner which gave Ryan no chance.
Australia pushed forward in response and appeared to have claimed a vital win when Mooy swept home his first goal in over two years for the Socceroos in the 79th minute.
Australia's third draw of the campaign in eight matches has left no margin for error heading into the last two matches against Japan and the Saudis.
With Japan to play last-placed Vietnam at home in their final match and Saudi Arabia away to struggling China in their other remaining fixture, it's almost certain Arnold's men will have to qualify via the playoff route with anything less than two wins.
"We have to win both games," Arnold told Network 10. "Beating Japan and beating Saudi Arabia away, our goal differences is like an extra point.
"I just said to the boys they've got to get themselves ready, go back to their clubs and work hard and come back in great fashion."