The Brumbies, under-rated all season, looked off the pace at the breakdown but two penalties from Holmes and a long-range effort from Jesse Mogg gave the visitors a 9-5 lead at halftime.
However, the Waratahs saw immediate benefit from a new backline combination and an attacking mindset, with Tatafu Polota-Nau crashing over in the first half and Berrick Barnes forcing his way over in the 57th minute to give the Waratahs a 15-9 lead.
But in the end, it was to no avail, with the Brumbies showing composure under pressure before Holmes threw a looping long ball for Speight to score the vital try.
The Brumbies missed out on the bonus point which would have guaranteed them a home playoff.
If teams are locked on points at the end of the regular season, it comes back to most wins and at the moment the Brumbies and Reds are locked on 10 wins each.
Queensland also remain a chance to still force a wildcard finals spot, as would the Brumbies if they lose to the Blues and the Reds take maximum points over the Waratahs.
Brumbies 19 (H. Speight try; Z. Holmes con, 2 pens, J. Mogg 2 pens), Waratahs 15 (B. Barnes, T. Polota-Nau tries; Barnes con, pen). Halftime: 9-5.
- AAP