Juan Cala scored the only goal of the game at St Mary's and the result has seen the Bluebirds close the gap on 17th-placed Norwich City to just four points.
Solskjaer said after the game that he believes the result has given his side hope of staying in the Premier League.
"It was a great performance, and this time we got that bit of luck that you need in a game," the Norwegian told the club's official Twitter account.
"All the lads were fantastic. The lads were galvanised and the atmosphere in the dressing room then was excellent.
"Nobody expected us to win here. We beat a very good side today and we're back in the fight."
Cardiff's next game sees them host Stoke City at the Cardiff City Stadium a week today.