Mauricio Pochettino's team went down 4-2 when the sides met in a fiery north London derby on December 2, but Alli's impudent finish in the 59th minute added to Son Heung-min's opener to send Spurs into the final four for the first time since 2014-15.
A banana was thrown on the pitch after Pierre-Emerick Aubameyang scored a penalty in the teams' previous encounter and on Thursday (AEDT) Alli was hit by a bottle thrown from the stands, responding with a '2-0' gesture to the fans.
Unai Emery - who left Mesut Ozil out entirely for "tactical reasons" - may step up his interest in defensive reinforcements after his makeshift backline was twice punished by clinical Tottenham counter-attacks in their second straight defeat.
Henrikh Mkhitaryan was unable to beat Paulo Gazzaniga from 12 yards when one on one and Son punished him in the 20th minute, curling past Petr Cech after Granit Xhaka – deployed at centre-back – played him onside.
