Les Bleus were handed a scare when Craig Goodwin opened the scoring for Australia within nine minutes, but two historic goals for Giroud alongside headers from Adrien Rabiot and Kylian Mbappe eventually saw France see out a routine victory.
Bedevilled by absent players both before and after travelling to Qatar, France's injury problems were exacerbated with only nine minutes on the clock, and this one also came with insult.
Australia winger Mathew Leckie got the better of Lucas Hernandez on the right-hand side and crossed for Goodwin to fire into the roof of the net at the far post, but Hernandez went down clutching his knee and stayed down.
The Bayern Munich man hobbled off with assistance from the medical staff to be replaced by brother Theo Hernandez, and Australia initially did well to keep France's attacking powers at bay.
However, Les Bleus started to turn the screw and were level on the 27-minute mark, as Hernandez junior whipped in a delightful cross for the unmarked Rabiot to head home past Mat Ryan and restore parity for the world champions.
Didier Deschamps's side suddenly had their tails up, and Australia defender Nathaniel Atkinson learned a harsh lesson after losing the ball to goalscorer Rabiot close to his own goal in the 32nd minute.
Rabiot stole the ball off Atkinson on the left before playing a one-two with Kylian Mbappe and finding Giroud inside the box, and the AC Milan veteran had the simple task of finishing into an empty net for his 50th international goal.
Antoine Griezmann and Ousmane Dembele then missed chances for France before Mbappe somehow fired over from a few yards out in the 45th minute - rivalling Andreas Cornelius for miss of the day - as Australia soon found themselves under constant waves of pressure.
Graham Arnold's men very nearly scored an unexpected equalizer in first-half injury time, though, with Jackson Irvine's header leaving Hugo Lloris stranded and clipping the post on its way behind.
Within just six minutes of the second half, Giroud connected with Hernandez's cross with an eye-catching bicycle kick as he attempted to net his latest trademark screamer, but his acrobatic effort went harmlessly wide.
France were denied a third in the 67th minute when Aziz Behich made a terrific goal-line clearance from Griezmann's strike, but Les Bleus would increase their lead only one minute later, as Mbappe headed home off the post from Dembele's cross.
Only four minutes later, Mbappe turned provider for Giroud to score a historic fourth, bursting down the left and crossing for the 36-year-old to head home his 51st France goal - equalling the all-time men's record set by Henry.
Giroud would not be setting a new record on Tuesday night as he was taken off in the dying embers, just before Ryan had to be alert to beat away an Ibrahima Konate header at the start of seven minutes of injury time.
Deschamps's side remained untroubled en route to an opening three points and now prepare to meet Denmark on Saturday, while Australia will aim to bounce back when they tackle Tunisia on the same day.