Level on seven points in Group 1 with Qatar and Iraq before the match, Australia scored twice through Blackburn Rovers star Brett Emerton before a 75th minute strike by Liverpool's Harry Kewell earned them a well-deserved victory in windy conditions at the Al Sadd Stadium.
Ibrahim Khalfan scored a consolation goal for Qatar in the 90th minute, but that was the only bright spot for the hosts who were unlucky to miss several chances, especially in the first half.
Australia's win puts them on top of their group with 10 points leaving Iraq and Qatar, both on seven, to battle it out for the second spot when they clash in Dubai on 22 June. China, the other team in the group, are already out of contention after suffering a 2-1 defeat at the hands of Iraq in Tianjin on Saturday.
The win was Australia's first in an away game and came after coach Pim Verbeek had copped a great deal of criticism for his conservative strategy while playing abroad, especially after their 1-0 defeat to Iraq earlier in the week in Dubai.
Nervous moments for Australia
Australia survived a few anxious moments in the first few minutes of the game - a Wesam Rizq free kick in the second minute testing goalkeeper Mark Scwarzer -- but began stamping their authority over the proceedings and putting the Qatari defence under pressure. The Socceroos soon found the net when Mark Bresciano cut in from the left and found Emerton, who easily placed the ball into the net from the far post after Kewell had failed to connect in the centre.
Qatar's Uruguay-born striker Sebastien Soria Quintana was a constant threat to the Aussie defence and despite heavy marking was able to produce some of his trademark runs into the danger area, forcing Schwarzer to be at his best.
Qatar desperately looked for the equaliser with Quintana coming close in the 40th minute after Schwarzer had left his position, but the striker's shot went wide. Moments later, Schwarzer was lucky to get to the ball a fraction faster than Quintana as Australia heaved a sigh of relief and went into half-time with their lead intact.
Australia raised their game a notch in the second half and consolidated their position when Kewell beautifully flicked the ball towards the onrushing Emerton, who found the left corner of the net with the Qatari goalkeeper Mohammed Saqr standing no chance.
Qatar's defence was once again in tatters in the 75th minute when Brett Holman's cross found the Aussie skipper Kewell, who scored with ease. A couple of minutes earlier Schwarzer was booked for wasting time and will miss the Socceroos home match against China.