Stephen Humphrys sent Rochdale in level at the break after Son Heung-min had given Spurs the lead, but a hat-trick from Fernando Llorente and further efforts from Son and Kyle Walker-Peters ensured that the Premier League side were able to coast into the last eight, where they will face Swansea City.
However, the game was not without controversy as VAR was used to rule out a Spurs goal and award the North Londoners a penalty in the first half, which was then disallowed after the official deemed that Son had halted his run before finding the back of the net.
The first talking point occurred in just the sixth minute when Erik Lamela converted from close range after Son had seen a shot well saved by Josh Lillis, but despite the goal initially being given, it was soon chalked off through VAR with Llorente harshly being deemed to have committed a foul.
Rochdale rallied, with Matt Done volleying just wide of the far post after latching onto a diagonal ball, but Spurs eventually went ahead when Son cut inside onto his right foot before finding the bottom corner from 12 yards.
The second controversial moment of the first half came when Kieran Trippier was fouled when running into the penalty area and, although a free kick was initially given on the edge of the box, VAR determined that the infringement was still taking place inside the area.
Son took responsibility for the spot kick but, although the South Korean international found the bottom corner, the referee chalked his effort off - and handed out a yellow card - after deciding that the attacker had halted his run completely before hitting the back of the net.
As the first half neared a conclusion, Lillis stayed big to block from Lamela and save from a Llorente header, but just before the break, Cannon struck the far post after drilling a low effort past the outstretched hand of Vorm.
However, after the restart it was one-traffic in Spurs' favour, with Llorente's first coming in the 47th minute as the forward dinked the ball over Lillis after latching onto a through-ball from Lucas Moura.
The January signing also provided the assist for Llorente's second, with his pass across goal being poked into the far corner by the former Swansea City man.
Llorente's hat-trick was complete when Son floated the ball into the six-yard box, where the Spaniard was able to rise above a defender to nod into the corner from close range.
Shortly after the hour mark, Son finally got his second of the game when Llorente picked out his run into the penalty area to give his teammate the chance to tap into an empty net.
Spurs went through the motions during the final quarter of the game, even though Mauricio Pochettino opted to introduce both Mousa Dembele and Dele Alli when he could have potentially given the pair the night off.
Alli should have netted a sixth for Spurs but after Lamela had struck the post with a 25-yard free kick, the substitute directed the ball straight at Lillis from inside the six-yard box.
Ian Henderson nearly added a consolation goal for Rochdale in the final 10 minutes when getting a header on target from close range, but Spurs were still able to score a late sixth when Walker-Peters received a pass from Alli before forcing the ball past Lillis for his first goal for the club.
TOTTENHAM HOTSPUR (4-2-3-1): Vorm; Trippier, Dier, Foyth, Rose; Sissoko, Winks (Dembele 62'); Lamela, Son (Alli 67'), Lucas (Walker-Peters 82'); Llorente
ROCHDALE (4-4-2): Lillis; Rafferty, McGahey, McNulty, Delaney; Done, Cannon (Adshead 76'), Camps, Kitching (Thompson 64'); Humphrys (Davies 58'), Henderson