Giroud has been linked to Everton, West Ham and Marseille during the close-season and was identified as a possible target for Borussia Dortmund if 2016-2017 Bundesliga top scorer Pierre-Emerick Aubameyang moves to Chelsea.
The France international began a burst of three goals in the space of 11 minutes after the half-hour mark at ANZ Stadium, where Aaron Ramsey and Mohamed Elneny were also on target.
Egypt midfielder Elneny hit the bar with a sumptuous strike during the second half, while Steven Lustica's consolation offered scant threat to Arsene Wenger's side, who made it two wins from two on the Sydney leg of their pre-season tour.
The arrival of Alexandre Lacazette has done much to increase uncertainty around Giroud's immediate prospects and, having marked his debut against Sydney FC with a goal, Arsenal's club-record signing engineered space with some slick footwork to draw an early stop from Vedran Janjetovic in the Wanderers goal.
Lacazette's touch let him down after Robert Cornthwaite got caught under a deep Alex Iwobi cross and the hosts' defender recovered to block the shot.
Giroud found the breakthrough in the 33rd minute after Nacho Monreal burst into the box down the left, with his cutback coolly lifted into the roof of the net.
Monreal was the provider once again four minutes later when his raking pass caught out a high Wanderers defensive line, allowing Ramsey to scamper clear and lift a finish over Janjetovic.
The host was entitled to feel a little hard done by when Elneny's shot squirmed over the line via a deflection off Brendan Hamill, although the former Basel man almost had a goal to reflect more fondly upon when his dipping 25-yard effort cannoned off the bar with Janjetovic rooted to the spot.
Arsenal conceded an indirect free-kick inside their area in the 57th minute and Lustica beat the massed ranks on the line at the second attempt.
Wenger made 10 second-half substitutions and Theo Walcott drew a superb stop from Janjetovic in the final minute, in between the upright denying Mesut Ozil and youngster Eddie Nketiah.