Mauricio Pochettino's team went down 4-2 when the sides met in a fiery north London derby on 3 December (AEDT), 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 2014-2015.
⚽️ GOAL!! "That is a DELICIOUS finish!!" 😋 @dele_official with a touch of genius!! @Arsenal 0️⃣-2️⃣ @SpursOfficial | Watch LIVE on beIN 2 and CONNECT ▶️ https://t.co/uUqSK5Bx8K #CarabaoCup #ARSTOT pic.twitter.com/enbnzsEFRh— beIN SPORTS (@beINSPORTS_AUS) December 19, 2018
A banana was thrown on the pitch after Pierre-Emerick Aubameyang scored a penalty in the teams' previous encounter and Alli was hit by a bottle thrown from the stands in this match, responding with a '2-0' gesture to the fans.
Disgraceful!! 😡 A bottle thrown from the crowd in the direction of @dele_official clearly strikes him on the head, and he responds superbly!! 0-2 | Watch LIVE on beIN 2 and CONNECT ▶️ https://t.co/2dqU4scKly #CarabaoCup #ARSTOT pic.twitter.com/7bAwD0LV7O— beIN SPORTS (@beINSPORTS_AUS) December 19, 2018
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 Spurs counter-attacks in its 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.
⚽️ GOAL!! Here comes the Son 🌞 After all the pressure, it's Spurs that goes ahead!!! @Arsenal 0️⃣-1️⃣ @SpursOfficial | Watch LIVE on beIN 2 and CONNECT ▶️ https://t.co/AZ3HsprOKI #CarabaoCup #ARSTOT pic.twitter.com/boRYN38iG8— beIN SPORTS (@beINSPORTS_AUS) December 19, 2018
Moussa Sissoko contrived to blaze over at the end of a rapid Tottenham break that followed Lucas Moura's tackle on Mkhitaryan, but Gazzaniga kept the visitors ahead by tipping Aaron Ramsey's shot against the upright two minutes before the break on the Welshman's 350th Arsenal appearance.
Emery switched to a back three with the introduction of Laurent Koscielny at half-time but the centre-back, still working his way back to full fitness after an Achilles rupture in May, played Alli onside and the 22-year-old poked a delightful finish past a stunned Cech.
Alexandre Lacazette hit the post soon after replacing Alex Iwobi, while Aubameyang saw a cross from the left hit the bar after Alli appeared to be struck by a bottle thrown from the crowd.
Arsenal was unable to find a way back into the game, with Gazzaniga not having to make another save before the final whistle.
Pochettino clearly wants to win the first trophy of his Tottenham career. Having joked that Harry Redknapp's triumph in reality TV show I'm a Celebrity … Get Me Out of Here! represented silverware for Spurs, the manager said in his pre-match news conference that any title would show the "value" of the work being done at Spurs.
Although he left Harry Kane out of his starting line-up, the only high-profile omission in his XI, he sent the England star on with over 30 minutes remaining and just 66 seconds later he supplied the assist for Alli's goal.
Arsenal welcomes Burnley to Emirates Stadium in the Premier League's early kick-off on Saturday, while Spurs head to Everton a day later.