(AFP) - The victory -- Leverkusen's 17th in 18 fixtures this season -- reestablished their two-point lead over second-placed Bayern Munich.
Xhaka joined Leverkusen in the close season from Premier League side Arsenal, where he played under Alonso's childhood friend Mikel Arteta.
"It's a dream for me to play under Xabi Alonso, he was a world-class player in the same position as me -- I played against him myself," Xhaka told Sky Germany.
"He gives me things that I can take...
"We have a great team, a great coach and a great mentality.
"We work hard daily and you can see the results on the ground."
Xhaka is one of several summer signings to impress this season, along with Alex Grimaldo, who scored in the win over Bremen, Victor Boniface and Jonas Hofmann.
Leverkusen's blistering start has some talking of a potential maiden Bundesliga title, but Xhaka was careful not to look too far into the future.
"Nothing is a foregone conclusion. We need to continue to work and see where we end up," he said.
"In football, anything is possible.
"We must continue to keep our feet on the ground and we will see what will happen."