The Saints suffered a bad defeat at Rotherham in the Carling Cup in midweek but made amends with a happier return to South Yorkshire.
But they enjoyed a slice of good luck with strikes which came from an unfortunate own goal and a disputed penalty.
Doncaster only have themselves to blame after missing chances - none more blatant than in the fifth minute when Jason Price fired straight at visiting keeper Kelvin Davis when he should have fired into the net.
Richie Wellens had put him clean through and Price had only the keeper to beat with Southampton hesitating expecting an offside flag which never came.
But the Rovers striker panicked as Davis advanced and fired straight at him when he could have curled his shot into either corner.
Both teams were always looking to attack and the Saints pushed plenty of players forward working tremendously hard and playing some skilful football.
A super inter-passing move between David McGoldrick and Andrew Surman almost led to a goal in the 16th minute, but McGoldrick's final shot lacked pace and home keeper Neil Sullivan saved.
Sullivan came to the rescue again in the 17th minute to keep out a fierce angled drive from Surman, before Davis dived full-length to tip away a goal-bound header from Darren Byfield.
Doncaster were rocked five minutes after the interval when Southampton snatched the lead with Saints defender Matt Mills turning a cross from McGoldrick into his own net as he tried to clear the danger.
Southampton's second came eight minutes later when Surman tapped home a penalty into Sullivan's left-hand corner after Wellens was harshly judged to have brought down Adam Lallana.
It could have been worse for the home side when Southampton were awarded another penalty ten minutes from time after Sam Hird brought down Surman from behind.
Surman tried to place the spot-kick in the same corner, but Sullivan was alert and dived to make a fine save.