The Lions led 27-3 at the break and were never seriously threatened by an under-strength Force outfit.
Halfpenny got the ball rolling after just two minutes with his first shot at goal before Irish pivot Jonny Sexton dummied his way over the tryline to score the 2013 Lion's first try on Australian soil. Halfpenny converted to put the Lions out 10-0.
The Lions dominated possession for the next 20 minutes but were repelled by stubborn defence. Eventually Brett Sheehan pegged the score back to 10-3 on 32 minutes.
O'Driscoll outpaced the Force defence and touched down in the corner before England flanker Tom Croft crossed for another try wide out after the siren, which Halfpenny again converted, to give the Lions a commanding 27-3 half time lead.
The second half was only two minutes old when impressive No 8 Jamie Heaslip dotted down wide out.
The home crowd finally had something to shout about a couple of minutes later then No.8 Richard Brown powered over to give Sheehan a straight forward conversion.
Mako Vunipola and Tommy Bowe kept the scoreboard attendant busy with further tries before the Force stopped the one way traffic through replacement Lachlan McCaffrey who forced his way over for the hosts in the 63rd minute to bring it back to 48-17, with Sheehan landing the conversion.
But O'Driscoll quickly replied with his second of the night before replacement fly half Owen Farrell scored a minute later with Halfpenny landing both conversions from straight in front.
Welsh lock Alun Wyn-Jones received a yellow card for slowing the ball down in the 71st minute but it didn't deter the Lions from finishing on a high with English lock Geoff Parling diving over for a try. Halfpenny completed a perfect night with his ninth conversion for a haul of 24 points.
The Lions' next match is against the Reds in Brisbane on Saturday.
Force:Tries: Richard Brown, Locky McCaffrey; Cons: Brett Sheehan (2); Pen: Sheehan
British and Irish Lions: Tries: Jonathan Sexton, Brian O'Driscoll (2), Tom Croft, Jamie Heaslip, Mako Vunipola, Tommy Bowe, Owen Farrell, Geoff Parling; Cons: Leigh Halfpenny (9); Pens: Halfpenny (2)