Mourinho's decision to replace Juan Mata and Andre Schurrle with Willian and Oscar turned out to be a wise one.
Oscar's deflected shot rebounded off a post into the path of Fernando Torres, who put Chelsea ahead.
Willian doubled the lead 11 minutes later and Oscar wrapped up the win eight minutes from time.
Southampton had held their own for the majority of the first half, but Oscar's trickery proved too much for the south-coast side, who have now won once in their past nine matches.
Oscar did blot his copy book when he dived in an attempt to win a penalty following the slightest of touches from Southampton goalkeeper Kelvin Davis.
Mourinho admitted Oscar deserved his caution, but insisted the Brazilian was not a serial diver.
"Oscar is a clean player," Mourinho said.
"He was waiting for the goalkeeper to come and smash him because that's what normally happens in those situations.
"It happened with Oscar at West Ham but the goalkeeper stopped before the contact so in the end instead of the goalkeeper trying to smash him it was (Oscar) trying to touch the goalkeeper. It was a fair yellow card."
The result keeps Chelsea within two points of Premier League leaders Arsenal, but Mourinho suggested his team are not contenders for the title.
"We are not candidates," he said.
"We are just candidates to win always the next match - and the next match is Hull City for the Premier League.
"I keep saying I know what I am building at the club. I know that next summer will be a moment for us to go to a couple of clinical buys to improve definitely our team in that direction but at this moment we work, we improve, we try to bring in people like Eden Hazard, Willian and Oscar to a different level of playing football and I think we are doing that quite successfully."