The Dutchman, who moved to the Merseyside club for a reported fee of £75million in January was greeted with boos every time he touched the ball in what turned out to be an easy victory for his new club.
Roberto Firmino gave Liverpool an early lead with an assured finish after Mohamed Salah pounced on a mistake by Wesley Hoedt.
The hosts forced good saves from Loris Karius in the first-half, but the contest was all sewn up when Firmino’s wonderful flick let in Salah who bagged his 29th goal of the season just before the break.
The return of van Dijk gave the fixture added spice going into the game, but it turned out to be a fairly straightforward afternoon for him and Liverpool.
And the centre-back insisted he was not fazed by the chorus of boos that greeted him when he touched the ball.
In an interview with Sky Sports after the game, van Dijk said: “I just focused on the game. I enjoyed being back and there are a lot of good memories here.
“You can’t do anything about the reception, you just do your thing.”
Defeat sees Southampton fall into the relegation zone after Newcastle’s surprise win over Manchester United and Saints manager Mauricio Pellegrino insisted his side’s situation can change in a matter of weeks.
He said: “It’s emotional for a lot of people. It’s tight in the Premier League and the teams can change around.
“We will try to win the next game and until the end we will be there.
“In football everything can change in a few weeks.”
Pellegrino also lamented his side’s confidence and self-belief after Liverpool’s second goal.
He added: “It was really difficult because we conceded on the counter-attack, where they are really dangerous.
“We then created two or three chances but after their second goal our team were a little bit harmed in their self-confidence and belief.
“We couldn’t show what we are about, it was too much for us.
“We just needed to score one goal to get back in it.”