The Wallabies winger crossed twice in the opening 15 minutes and grabbed his third touchdown nine minutes after the break as the visitors defended stoutly to cement top spot in the Australian conference.
The Waratahs battled to the finish but their fourth defeat of the season leaves their playoff hopes in jeopardy.
"Very happy with that. I thought the last 20 minutes we defended really well," Brumbies co-captain and hooker Stephen Moore said in a pitch-side interview at the Sydney Football Stadium.
It has been a sombre week for the Canberra side during which their bullocking number eight Ita Vaea was forced to retire due to a heart condition.
"We spoke a lot about Ita," Moore added. "I said to the boys before 'just play as if it's your last game' and that's what we did."
The Brumbies jumped into a 12-0 lead with the enterprising Tomane crossing at the right corner twice before the Waratahs had settled.
Winger Reece Robinson touched down for the home side's first try in the 21st minute and the new pairing of centres Israel Folau and Kurtley Beale began to cause headaches for the Brumbies defence.
A jinking midfield break by Beale set up the second Waratahs try nine minutes before halftime, with regular fullback Folau burning over the line near the left corner after taking a superbly weighted pass from fullback Andrew Kellaway.
Wallabies skipper Moore grabbed back the lead for the Brumbies a few minutes later, bustling over from a maul, with Christian Lealiifano's conversion giving the visitors a two-point lead at the break.
Nine minutes after the restart, Aidan Toua floated a long ball over to Tomane who cantered five metres to touch down for his third try near the right corner and celebrated his second career hat-trick.
The Brumbies kept the Waratahs from scoring for nearly half an hour until Bernard Foley slotted a 77th-minute penalty to peg the deficit back to six points.
But a gallant effort to score a length-of-the-field try, after the final siren, was dashed when replacement prop Paddy Ryan coughed up the ball in a tackle behind the Brumbies' 22-metre line.
(Reporting by Ian Ransom in Melbourne; Editing by Tony Jimenez)
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