Two excellent goals from Son Heung-min and a debut goal from Arnaut Danjuma were enough to send Tottenham through to the FA Cup final.
Spurs were frustrated by their Championship opponents until the 50th minute, when Son unleashed a 30-yard bomb.
In torrential rain, the South Korean international then turned and finished smartly to double the lead.
Danjuma, who joined on loan from Villarreal this week, scored after coming on as a late substitute.
Antonio Conte’s team has been drawn for the fifth round, which will take place on Monday evening.
