Dusan Tadic's opener, a placed effort following Ryan Bertrand's marauding run, and Polish defender Jan Bednarek's left-footed shot looked to be lifting Saints out of the bottom three.
But, with Mark Hughes seemingly on course for a first league victory as Southampton manager since arriving on 14 March, Giroud sparked a listless Chelsea into life.
The France forward's header - his first league goal for Antonio Conte's team - and left-footed drive sandwiched Eden Hazard's left-foot finish as the Blues moved within seven points of fourth-placed Tottenham.
For an hour, Chelsea's performance epitomised their travails since the turn of the year, with the defending champions having collected just 12 points from a possible 33.
Willian's 55th-minute shot was their first effort on target, and there were question marks over the application of several players in the build-up to both Saints goals.
One of those players - wing-back Marcos Alonso - was also fortunate to escape without punishment for standing on the back of Southampton forward Shane Long's calf in the first half.
After being sacked by Stoke, Hughes is facing the ignominious prospect of playing a part in the relegation of two clubs this season.
The upturn in results the Saints board hoped for when the Welshman was brought in to replace Mauricio Pellegrino just over a month ago has not materialised.
While an FA Cup semi-final against Chelsea is on the horizon, Hughes has presided over three successive league defeats, with three goals conceded in each match.
Following an abject 3-0 defeat at West Ham, there were encouraging signs in a 3-2 defeat at Arsenal last Sunday, and more of the same against Chelsea.
Southampton controlled proceedings for about 70 minutes, but their biggest problem is turning performances into points.
One victory in 20 league matches - against bottom club West Brom - does not bode well for the Saints, who could be six points adrift of safety later.
Conte changes the flow
Much of Chelsea's display typified the problems that have undermined their defence of the title and have been exacerbated by speculation over the future of Conte.
The Italian has not helped himself at times, allowing himself to become embroiled in a public spat with Manchester United counterpart Jose Mourinho and at times cutting a desolate figure on the touchline.
There was again an absence of emotion and touchline theatrics that marked first season at Stamford Bridge, but Conte did turn this contest on its head with the introduction of Giroud and Pedro.
Chelsea lacked conviction in front of goal until Giroud replaced Alvaro Morata, while Davide Zappacosta had a largely forgettable afternoon before being replaced by Pedro.
The former Torino man was caught out of position for Tadic's opening goal and had just 11 touches in Southampton territory during the first period.
By contrast Ryan Bertrand created the opening goal for Saints and appeared to be almost permanently stationed in the Chelsea half, having 23 touches.
Giroud, though, made the difference - scoring twice from his two efforts on goal. AGENCIES