Two goals in as many minutes from Patrik Schick and Karim Bellarabi gave Leverkusen the lead before Modeste's goals for Leverkusen.
Both teams already had — along with Bayern Munich — the best attacks in the league (nine goals from three games).
He follows fellow wideman Andros Townsend and goalkeeper Asmir Begovic to the blue half of Merseyside with new manager Rafael Benitez.
A first-half goal from Guido Burgstaller fired Schalke to a 1-0 victory over Wolfsburg and a place in the semi-finals of the German Cup.
Champions Bayern Munich opened the 2017/18 Bundesliga season with a 3-1 win over Bayer Leverkusen on Friday.