Wilson, who spent last season out on loan at second-tier Derby, hit a 25-yard screamer in the 53rd minute to add to first-half goals from Brazil star Roberto Firmino and an own-goal by Joachim Andersen.
The game was European champions Liverpool's last game before they face Manchester City in the season-opening Community Shield at Wembley this weekend.
Liverpool also welcomed back top scorer Mohamed Salah who was playing his first match of the pre-season after a break following the recent Africa Cup of Nations.
Klopp said it was too early to say whether or not Firmino, playing for the first time since the Copa America, or Salah would start against City on Sunday.
"I don't say 100 per cent not, there's a chance that they will play, yes. We have to see how they react tomorrow, now training is not the highest intensity anymore, now training is about the detail," Klopp told liverpoolfc.com.
Chelsea's Pedro also scored a goal to remember with a back-heeled volley from a Ross Barkley cross as Chelsea downed Salzburg 5-3.
Christian Pulisic scored twice in the Londoners' rout witRead More
