The first-half score from Auckland-born Lealiifano set the Australian outfit on their way to victory over the out-of-form Blues, who are coached by former Brumbies boss David Nucifora.
The New Zealanders felt the absence of Josevata Rokocoko as the hosts lacked penetration from the back line.
But the forward play and defence shown by the visitors, and their experience - the Brumbies started with seven Australia internationals - proved the difference.
Stirling Mortlock scored an early penalty before playing a pivotal role in Lealiifano's try after 31 minutes.
Mortlock added the conversion to stretch the Brumbies' lead, although Nick Evans put some points on the board for the hosts to reduce the deficit to 10-3 at half-time.
Mortlock and Evans then exchanged penalties in the second half, before Mark Gerrard also slotted over for the Brumbies to keep them comfortably ahead.
The Blues finally got their game together in the last five minutes when Rudi Wulf crossed the line, but it was too little too late and the Aucklanders' semi-finals hopes took another blow with their second home defeat of the campaign.