Khalfan Ibrahim gave Qatar a surprise 22nd-minute lead in Canberra before Khalil hit back with the first of his goals.
The striker's free-kick early in the second half then found the bottom corner before Mabkhout also netted twice.
Poor defending led to that opportunity, and Qatar's disorganisation meant Mahdi Ali's men looked dangerous going forward.
UAE playmaker Omar Abdulrahman was particularly dangerous in the opening 20 minutes, finding space in front of Qatar's defence.
But it was Qatar who struck first.
UAE were almost level in the 26th minute, only for Burhan to do well and deny Khalil's header.
While UAE perhaps should have had a penalty, Abdelkarim Hassan almost doubled Qatar's lead with a powerful long-range drive that went just wide.
Qatar failed to deal with an attack and Khalil's header was cleared off the line, but that rebounded off him and into the net.
The striker's second goal arrived seven minutes after the interval.
Khalil's free-kick from just outside the the box found the bottom corner, although Burhan probably should have done better.
Burhan spilled Khamis Esmail's long-range free-kick and Mabkhout was on hand to tap in.
Mabkhout sealed his team's win after a counter-attack, sweeping in an Abdulrahman pass from close range in the 89th minute.
