Van Dijk scored a header from a corner for Liverpool's first goal.
The Dutchman bullied Fred and Brandon Williams in the area - who were marking zonally - as the cross came in, before heading past David de Gea.
He said: "We tried to find the near post and it worked. Fantastic delivery and the timing was there. I'm delighted. It's never easy - today I was marked by two opponents.
"We had chances today. We had to find a way through. You need to find the right spaces and throw your body on the line."
Liverpool had a goal ruled out following Van Dijk's opener after the Dutchman was adjudged to have fouled De Gea in the build-up.
On the decision, Van Dijk added: "I didn't jump with my hands up [on De Gea] - it's difficult.
"If VAR gives it we just have to accept it and carry on. I didn't think it was a foul. I expected it to be a goal."