The tepid early sparring gave way to a glimpse of what was to come when a smart Lucas Moura through ball picked out Harry Kane, and Alphonse Areola was equal to his powerful effort in the West Ham goal.
The Hammers launched an immediate onslaught of Hugo Lloris’ goal, Tomas Soucek twice forcing the Frenchman into sprawling saves on a rare Carabao Cup outing.
Jarrod Bowen found the way through moments later, twisting in the Tottenham box and firing low into the corner - as West Ham made do without the Covid-stricken Michail Antonio.
And yet, Spurs were back ahead by the 35th minute as Bergwijn took it upon himself to burst forward and roll a cutback for Moura, who made no errors with his simple finish.
The second-half saw Conte show his ruthless side and unapologetically sit his team in for the win, sending on Harry Winks for the excellent Bergwijn.
David Moyes’ visitors were unable to find another route to Lloris’ goal as the Hammers, who downed both Manchester City and Manchester United en route to the final eight, must continue to wait for a first trophy in over 40 years.