Yet Rangers made the worst possible start by conceding a goal after only 57 seconds.
Goalkeeper Lee Camp handled outside the area and, from the free-kick taken by Adam Hammill, Darren Powell bundled the ball over the line.
Southampton should have scored a second in the 36th minute but for a grotesque miss by Stern John.
He was left with only Camp to beat after Bradley Wright-Phillips had left him with the goal at his mercy but shot hurriedly and high and it proved to be a costly blunder.
Within two minutes Rangers were level when the impressive Rowan Vine beat three players on the edge of the area to set up a simple scoring opportunity for Martin Rowlands.
Southampton were further punished when a long centre from the left by Damien Delaney eluded defender Jermaine Wright at the far post and Patrick Agyemang was able to turn the ball in from close range.
Southampton's caretaker managers Jason Dodd and John Gorman tried to change things around at the interval by introducing Marek Saganowski in place of Hammill but it was Rangers who scored again.
After 59 minutes a long kick downfield by Camp found defenders Wright and goalkeeper Kelvin Davis leaving it for each other allowing Agyemang to shoot into an empty net.
Southampton desperately attempted to find a way back into the match. They had influential midfield player Youssef Safri sent off for serious foul play after a clash with Agyemang.
Saints never gave up and set up a thrilling last four minutes of stoppage time when John partially made up for his first-half error by controlling a pass from Jhon Viafara and scoring from six yards.
But Rangers were in no mood to surrender and held on for the points.