Browning, who is a member of the Williams Driver Academy, overcame the best efforts of front-row starter Gabriele Mini twice on the run down to Lisboa to set up his dominant run to the chequered flag.
Off the original start, Browning got away well but Mini seized the opportunity of the slipstream to draft alongside his rival on the run to Mandarin and briefly swooped past into the lead.
But the Theodore Prema driver could not hold his advantage for long as Browning surged back ahead on the run to Lisboa – quickly eking out an advantage to end the opening lap 1.8 seconds clear.
Browning's lead was wiped away at the end of the second lap though after the safety car was called out following a collision involving Dan Ticktum and Ugo Ugochukwu at Lisboa, with both cars ending up in the barriers.
Browning got away well for the restart at the beginning of lap five of 10, but Mini got the tow again and tried to find a way past as the duo snaked their way down to Lisboa.
But as Browning held firm against Mini, it was Dunne, who had originally started sixth, who made the most of the restart opportunity to take the inside line against the cars ahead and grab second from Mini.
From there, Browning was again able to open up an advantage as he ended the lap 1.4 seconds clear of Dunne.
And although Dunne briefly appeared able to match the race leader’s times, even closing in by one tenth over the following two laps, Browning had everything under control and slowly edged clear over the remaining laps to win by 2.097s.
Mini had no response to the Hitech duo ahead of him as he steadily fell back, eventually finishing 2.3 seconds adrift to take third place, with his team-mate Dino Beganovic coming home right behind him to snatch fourth.
F2 driver Dennis Hauger eventually finished a lonely fifth, as he ended up 5.5 seconds adrift of the cars in front of him, with Mari Boya taking sixth and Paul Aron seventh.
Completing the top 10 were Pepe Marti, Isack Hadjar and Zane Maloney.
Macau GP - F3 qualifying race result
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