t, let alone three.However, a wonderful strike from the unlikely source of centre-back Juan Cala secured a 1-0 victory in a match dominated from start to finish by Saints.
It was only Solskjaer's third league win at the helm and one which still leaves his side 19th in the standings, but now just three points from safety.
"It was a good performance," the Cardiff boss said
"We've had some very good performances before that I've been proud of, but I have been sat here talking about bad luck and missed chances.
"But today, of course, we got that little bit of luck that you need in a game.
"They were all fantastic
They all did their jobs - every single one
It's not just the 11, it's the subs as well, even ones that don't come on and it's the ones that travel.
"The atmosphere in the changing room was great afterwards.
"Before today I don't think many expected us to come here and take points
We were six points behind, now we're three points behind.
"We have four games to go
Fulham, Swansea, Norwich and West Brom are still in it with us, but we've just got to do our job
We still need some help but it's been a wonderful week."
It has certainly been a fine end to a turbulent week, with last Saturday's embarrassing 3-0 home defeat to Crystal Palace compounded by claims their team had been leaked to the London club.
The Welsh club's chairman Mehmet Dalman has been in contact with the Premier League over the incident, which is understood to have seen Cardiff sack one member of staff and discipline another.
Solskjaer would not reveal the parties involved in the alleged leak and was keen to avoid talking about the issue at all after the win.
"We'll keep that within," he said
"We're dealing with it as a club and we move on.
"We've had issues, I've dealt with it and they (the players) just focus on the football
I can focus on the rest of it.
"We ended this week on a high and it is back to square one next week because it is about performing on the day."
Next up for Cardiff is a home clash with Stoke, while Saints travel to Aston Villa fresh from a frustrating home defeat.
Saints' dominance was highlighted by the fact they had 68 per cent possession, with this match just the sixth time Mauricio Pochettino's side have failed to score in a league game this season.
"What happened is that we didn't score a goal," the Saints boss said
"We created many chances, but we lacked a clinical edge that we actually needed to win the game.
"I think it was the easiest game we've had in terms of possession.
"We had loads of possession, long spells of possession, but in the end it's a steep learning curve when you realise that all that possession is useless when you don't score a goal, and that's what we learned
That's what happened."
The match was Southampton's first since Jay Rodriguez was ruled out for six months with a ruptured anterior cruciate ligament.
Saints showed their support for the England international by wearing number nine shirts ahead of a game in which his absence was clear.
"When you lose, you always miss the players that are out," Pochettino said
"That always happens.
"[The shirts were] the club's idea
It was basically everybody involved with the club had the idea to support him, and of course he has our full support in this really tough time that he is going through, and we want him to get better as soon as possible."
Source : PA
Source: PA