Brumbies coach White spoke earlier in the week about the need to start strongly against the visitors, who ended up fielding five new players in their starting side.
It was Tomane who answered the call just four minutes when the winger took an intercept and sprinted 80 metres for his first Super Rugby try.
It set the tone for the Brumbies, who scored again 10 minutes later after hard-working flanker Michael Hooper broke the line and dished the ball off to Tomane to cross for his second.
At one point the Brumbies were 17-3 up, before Colin Slade's goalkicking and Aaron Smith's try in the 35th minute kept the Highlanders in the game.
Minutes into the second half, a try to debutant Shaun Treeby had the Highlanders draw level at 23-23.
But in the 62nd minute, Hooper dragged two Highlanders over the line with him to push the Brumbies back into the lead, which they held onto in front of 12,269 spectators.
- AAP