Spurs took the lead in the 27th minute when Nacer Chadli curled home, before Eric Dier netted a deflected effort in the 64th minute.
Dier then added a second nine minutes after half-time, before Davies scored an own-goal in the 80th minute.
But Tom Carroll then added gloss to the scoreline by adding a fourth for the north London side late on.
Davies used his personal Twitter account to joke about opening his Tottenham goal-scoring account soon after the final whistle.
— Ben Davies (@Ben_Davies33) January 30, 2016
The result means that Spurs are the second team to book their place in the fifth-round draw after Manchester United’s win over Derby County on Friday night.
The north London side are now gearing up for their Premier League trip to Norwich City on Tuesday night.
MORE: The latest football news