The Hampshire side followed up that victory with a 1-0 win that condemned fourth-placed Cardiff to only their fifth defeat of the season.
Dutchman Wotte, who has given Southampton a fighting chance of staying up since replacing hapless fellow countryman Jan Poortvliet, led a post-match celebration huddle.
Wotte said: "You have to be united, that is very important and there is a great spirit in the team now.
"The players believe they can stay up and we have had two fantastic results and now we have to keep winning.
"Defensively we were excellent and this is our first clean sheet for some time.
"I am very proud of my team and the way they have been fighting for each other in the last few weeks."
Southampton had Cardiff defender Mark Kennedy to thank for taking the lead in the 11th minute when the veteran Irishman inexplicably handled Jason's Euell's right-wing cross.
Striker David McGoldrick calmly stepped up to take the resulting penalty, sending goalkeeper Dimitrios Konstantopoulos the wrong way and hammering his shot into the middle of the net.
In-form striker Marek Saganowski had missed an easy header before Southampton goalkeeper Kelvin Davis produced a contender for Championship save of the season.
Davis showed great reflexes to palm away Roger Johnson's powerful effort before somehow readjusting his body to claw Ross McCormack's follow up header behind for a corner.
Cardiff responded to a half-time dressing down from manager Dave Jones by producing a more spirited second half performance.
But it was Saints who came closest to extending their lead when Polish international Saganowski hammered against the crossbar from six yards in the 65th minute.
Cardiff should have been given the opportunity to snatch a point they scarcely deserved in the dying seconds when Chris Perry allowed the ball to roll down his arm inside Southampton's six-yard box.
Amazingly referee Kevin Wright failed to spot the infringement, unlike the majority of the 18,526 fans inside St Mary's.
Bluebirds boss Jones refused to blame Wright for the defeat and instead focused his frustrations on the visiting players.
Jones said: "I have got no complaints because we did not deserve to win.
"A few home truths have been said after the game, which have not been heard for a long time.
"We have come off the back of some difficult games and there is always fatigue, but we cannot use that as an excuse for the result."