Saints dominated the first half and could have been out of sight had Mane and Eljero Elia been more ruthless in front of goal while Jose Font hit the crossbar from close range.
Rangers grew in confidence after half-time and had chances themselves but as the game looked to be heading for a goalless draw, Mane found the top corner with a strike at the death to maintain Saints' charge for the top four.
Chris Ramsey, who was put in joint-charge with Kevin Bond following Redknapp's resignation on Tuesday, issued a plea for more flair from QPR before the game and duly recalled talented Moroccan Adel Taarabt for only his second start of the season.
Redknapp had declared Taarabt "overweight" back in October and while the forward showed some elegant touches, he failed to make the desired impact and was replaced in the second half.
Rangers were often clumsy in possession and struggled to service Charlie Austin, who once appeared the side's trump card in the battle for survival but now has just one goal in seven matches.
Southampton have also endured a dip in form of late, suffering consecutive defeats to Crystal Palace and Swansea, but this victory will revive their confidence as they sit third before Manchester United play on Sunday.
QPR remain second bottom of the table and the hunt for a new manager now looks even more urgent.
The first opportunity of the contest fell to the visitors as Elia was sent clear and with Rob Green rushing out to intercept, the winger shot first time but missed the target.
Taarabt gave the home fans something to cheer about as he danced round James Ward-Prowse, first with a Cruyff-turn and then a neat touch through the midfielder's legs, but Rangers failed to create any clear-cut openings early on.
Instead, it was Southampton who looked the more likely and Victor Wanyama should have broken the deadlock 15 minutes in when Richard Dunne's header dropped loose in the box, but the Kenyan skewed wide.
Elia and Mane continued to cause problems with their pace in behind and Green did well to parry the latter's shot wide before Fonte smashed Ward-Prowse's corner against the crossbar soon after.
Dunne was fortunate to avoid harsher punishment when he booted Elia on the edge of the area moments before the interval and Ward-Prowse bent the resulting free-kick wide.
Rangers enjoyed more possession after the break and came close to taking the lead when substitute Mauro Zarate, on for Taarabt, stretched to meet Matt Phillips' cross but was unable to generate any power on the finish.
Austin nearly found a breakthrough in the 73rd minute when he diverted Joey Barton's shot goalward from close range but Fraser Forster did brilliantly to react and push the ball over.
Both teams pushed forward in search of a winner in the latter stages but it was Southampton who stole the points as Mane wriggled his way around Steven Caulker and drilled his shot into the top corner.
There was time for more late drama as QPR had the ball in the net before the final whistle blew but the linesman had his flag up and the home fans were sent home disappointed again.
Source : PA