Trailing 12-9 at half-time, the two-time champion Brumbies hit back with two second-half tries to nudge out the Perth-based Force in a lacklustre opening match of the Australian Conference.
White took over at the Brumbies after they finished a dismal 13th last season and fielded a largely new-look young side.
Both sides traded penalties before Force edged ahead at halftime but the Brumbies got going when wing Jesse Mogg and fullback Robbie Coleman scored tries six minutes apart early in the second term.
James Stannard kept Force in the contest with a try in the 55th minute to get within two points but they bungled an attempt at a drop goal in the final minute which would have given them victory.
White, who coached the Springboks to the 2007 World Cup crown in France, said that although the Brumbies had started cautiously, the game was there for the taking.
"You can't just go through the motions and be scared," he said.
"Somebody had to make a move and I'm just glad we managed to get over the line."
Force coach Richard Graham rued the 10-minute spell when the Brumbies crossed for their two tries, saying the break in the Force's concentration ultimately cost them the match.
"For a large part of the game we played the way we wanted to play; we controlled the game," he said.
"But it was just that 10-minute period.
"I thought their breakdown work was good but we were probably a little bit slow."
The Brumbies have a bye next week, while the Force will face the Reds in Brisbane on Saturday (March 3).
Teams:Brumbies:
15 Robbie Coleman, 14 Henry Speight, 13 Andrew Smith, 12 Christian Lealiifano, 11 Jesse Mogg, 10 Matt Toomua, 9 Nic White, 8 Ben Mowen, 7 Ita Vaea, 6 Peter Kimlin, 5 Sam Carter, 4 Leon Power, 3 Dan Palmer, 2 Stephen Moore, 1 Ben Alexander
Substitutes: 16 Anthony Hegerty, 17 Ruaidhri Murphy, 18 Scott Fardy, 19 Michael Hooper, 20 Ian Prior, 21 Zack Holmes, 22 Joe Tomane
Force:
15. Alifeleti Mafi, 14. Nick Cummins, 13. Winston Stanley, 12. Rory Sidey, 11. Napolioni Nalaga, 10. James Stannard, 9. Brett Sheehan, 8. Ben McCalman, 7. David Pocock (captain), 6. Matthew Hodgson, 5. Nathan Sharpe, 4. Toby Lynn, 3. Salesi Ma'afu, 2. Nathan Charles, 1. Pekahou Cowan
Substitutes: 16. Elvis Taione, 17. Kieran Longbottom, 18. Phoenix Battye, 19. Angus Cottrell, 20. Justin Turner, 21. Ben Seymour, 22. Samu Wera