Saints lost six league matches out of eight to slip to 13th in the standings last month, seven points above the bottom three, and manager Ronald Koeman feared his side were being drawn into the relegation battle.
The upturn in fortunes has coincided with the return from injury of first-choice goalkeeper Fraser Forster, who has kept five successive clean sheets.
"We have a big game coming up against Swansea away and hopefully we can continue the form we are in," Van Dijk told the club's website (www.saintsfc.co.uk).
"Five clean sheets is amazing for the defenders and for the whole team. It gives us a lot of confidence being unbeaten. We have a run going on and we want to continue that."
Southampton travel to 16th-placed Swansea City in the league on Saturday.