The Socceroos did the damage in the first half, steaming to a 3-0 lead with the Qataris seemingly incapable of stemming a constant flow of attacks.
Giant Karlsruhe striker Joshua Kennedy opened the scoring on 11 minutes and Everton midfielder Tim Cahill and Palermo attacker Mark Bresciano gave the Australians a comfortable buffer before they coasted through the second half.
"We played a fantastic first half. We did really well, we created chances, we scored great goals and we didn't give them a chance to play football," Verbeek said afterwards.
"It was exactly what the plans were before the game and I am very proud of what they did, especially in the first half, because the quality was very high and they began to get tired in the second half, which we expected they would."
Roared on by 51,000 home fans, Australia could have won by more with only goalkeeper Mohammed Saqr preventing further damage in the first match of a tough section also containing Iraq and China.
The result vindicated Dutchman Verbeek's decision to focus on overseas-based players, with defender Craig Moore and John Aloisi the only representatives of the domestic league.
Moore was rock-solid in his final international match and was brought off with 12 minutes left to a huge ovation.
The Qataris, who arrived here a fortnight before the match, never recovered from their rocky start although they came close to scoring a couple of times in the second half. However, the Australians gave themselves a strong platform in their mission to qualify for the 2010 World Cup finals in South Africa.
The Socceroos began confidently and went ahead when Brett Emerton's cross from the right was headed in by German-based striker Kennedy. The 1.94-metre forward posed awkward aerial problems with Emerton and David Carney feeding him crosses from both wings before he came off with a foot injury in the second half.
The home team doubled their lead seven minutes later when Luke Wilkshire's corner was headed home by Cahill, who out-jumped Junior Amaral for his 13th international goal.
Australia were three-up in the 33rd minute when Bresciano sweetly volleyed home Celtic striker Scott McDonald's precision ball. The Socceroos could have been leading by far more at half-time with goalkeeper Saqr saving goal-bound shots by Cahill and Kennedy twice.
It was virtually one-way traffic in the first half with the Qataris' loose marking given Australia's midfield freedom to move the ball, which rarely came to home keeper Mark Schwarzer. Carney looked assured at left-back and passed with assurance, while Wilkshire and Jason Culina bossed the midfield.
Qatar coach Jorge Fossati made two changes at half-time, hauling off skipper Alshammari Sattam and Mahdi Saddiq to show his dissatisfaction at the limp performance. But the Australians kept on coming with Wilkshire having a fierce long-range volley fumbled for a corner by Saqr and a Cahill header just wide in the opening minutes of the second half.
Substitute Alhamad Mesaad had Qatar's best chance in the 58th minute but he side-footed past the left upright with the goal begging, while Yahya Ali Hassan had a shot saved by Schwarzer on the hour.