Spurs thought they had gone ahead in the eighth minute as Erik Lamela found the back of the net after goalkeeper Josh Lillishad spilled Heung-Min Son’s shot, but it was disallowed following a review by the Video Assistant Referee (VAR).
Son eventually opened the scoring in the 24th minute as he cut in on his right foot to unleash a low strike past Lillis from close range.
Stephen Humphrys brought Rochdale level in the 32nd minute after Andy Cannon played a ball over the top, which the former latched onto and fired home, 1-1.
The League One side gained a lot of confidence in the closing minutes of the first stanza, but neither side could add to the scorline and they went into break level.
Fernando Llorente restored the lead for Mauricio Pochettino’s men two minutes into the second half by turning home Lucas Moura's low cross from close range.
Spurs netted a third goal in the 53rd minute as Moura picked out Llorente, who finished with a clinical lob.
Llorente completed his hat-trick on the hour-mark with a header from point-blank range after being set up by Son.
Son then made it 5-1 in the 65th minute with a simple tap-in at the far post as the visitors were now completely falling apart.
Kyle Walker-Peters blasted home the sixth goal for Spurs in second-half stoppage time with a low strike from close range to seal a big win.
The North London outfit will now face Swansea City in the next round.