Spurs made 11 changes to their side, and that showed in a first half which saw the hosts take a shock lead right on the stroke of half time when Ian Henderson opened the scoring.
Lucas Moura marked his full debut with an equaliser after the interval before Harry Kane looked to have won it with a late penalty, but there was to be another twist in the tale as Steve Davies rescued a draw for Rochdale in stoppage time.
Find out how all of the drama unfolded courtesy of Sports Mole's minute-by-minute coverage below.
The visitors are the clear favourites heading into this match, but you never know with the FA Cup and League One strugglers Rochdale have the home advantage as they look to pull off a memorable cupset. Rochdale are one of only three lower-league sides still in the competition - and none are ranked lower than them - so they are doing this for the smaller teams as well today.
We will have a close look at both clubs in a short while, but first let's check out the team news...
The January arrival from PSG made his first appearance in a Tottenham shirt during the dying stages of the draw with Juventus in midweek, but he is included from the start today and will get a much better opportunity to give Spurs fans a first glimpse of what he can do.
It says plenty about Tottenham's strength in depth that they are able to make 11 changes from their midweek draw with Juventus and still put a side out with considerable quality - to the extent that one wouldn't bat an eyelid if perhaps eight of today's team were included in a Premier League starting XI.
However, there should still be plenty of attacking threat from the visitors as Fernando Llorente gets a run out up front, while Son Heung-min - who has been in superb form this season - also starts having missed out in midweek.
Speculation has begun to surface regarding Alderweireld's future after he was reportedly unhappy at being left out of the matches against Arsenal and Juventus recently, but Pochettino is keen to ease him back in to action and matches like today are perfect for that. The defender's only other appearance since the beginning of November was the replay win over Newport County in the last round.
Indeed, with Vorm also replacing Lloris in goal, the only defensive change from that replay victory in the fourth round comes at right-back, with Kieran Trippier starting in place of Serge Aurier this afternoon.
It will be interesting to see which role Sissoko plays this afternoon too, with the France international having featured centrally on occasions this term. Son and Lucas are also wide players, so it could be that Spurs adopt something closer to a 4-3-3 system this afternoon.
Experienced striker Calvin Andrew is still missing with an Achilles injury, while Keith Hill's options are further limited by Wiseman, Dobre, Knott and Hart all being cup-tied. As such, he makes just one change from Tuesday's defeat to Bristol Rovers as McGahey replaces Wiseman.
Winger Matt Done is also a threat, though, and is more than capable of weighing in with goals of his own too should Spurs take their eye off him today.
Pochettino claimed in his pre-match press conference that this test could be an even bigger one than recent matches against Arsenal and Juventus, but you'd have to think that if Spurs can avoid complacency then they will have enough to get past their hosts this afternoon.
The FA Cup run has provided a welcome distraction from league duties too, with Rochdale struggling badly on that front, sitting bottom of League One.
Dale would need to win all of those to make it to a position of safety - almost doubling their season tally of wins in the process - so it is highly unlikely they will make full use of them, but it is a lifeline nonetheless.
Keith Hill's side have only won three of their last 13 games across all competitions, losing seven of those in a run which stretches back to early December, but two of those wins have come in the FA Cup.
Doncaster awaited in the third round and were beaten 1-0 before Rochdale came up against their first higher-tier opposition of their run in the shape of Millwall in the last round. Dale needed a replay in that match, drawing 2-2 away before winning 1-0 in the return fixture here at Spotland.
However, none of those matches came against Premier League opposition and you have to go back to January 1971 for Rochdale's last FA Cup win against a top-flight team, losing all six such matches since then.
However, that solitary win did come in their most recent home game, and in this competition too as they beat Millwall. They have now won both FA Cup home games this season without conceding, and another victory today would see them win three in a row for the first time since January 2015.
It is an interesting decision from the hosts as on paper it looks like it takes an advantage away from them, and Spurs will certainly be happy that they have a decent surface to play on today.
Spurs are coming out of what looked like being a very difficult run of fixtures, facing Manchester United, Liverpool and Arsenal in successive Premier League games before taking on Juventus in the first leg of their Champions League tie on Tuesday. They took a hugely impressive seven points from those league games, though, and are now in the driving seat of their European tie.
Spurs must still negotiate the second leg at Wembley, which will still be a very difficult tie against the Italian champions, but those two away goals mean that the balance of the tie lies in their favour at the halfway stage.
Recent wins over Manchester United and Arsenal - in addition to their draw with Liverpool - have kept them right in the mix, and they are now very well placed to pounce should any of the current top four slip up at any point.
That includes three FA Cup matches so far this season, with Pochettino's side having beaten AFC Wimbledon in the third round before needing a replay to get past Newport County in the fourth.
Tottenham have not come up against opposition higher than League One so far in this season's competition, so it has been a relatively easy route as they look to reach the quarter-finals in consecutive seasons for the first time since 2001-02.
The most recent two of those have been impressive - against Liverpool and Juventus - but before that they were held at Southampton and Newport County, and they have now won just three of their last 13 outings on the road across all competitions.
Spurs may have made 11 changes to their side today, but it still looks like a good team for the visitors and I fully expect them to successfully negotiate this potential banana skin here. Rochdale will give it their best, but I cannot see that being good enough today.
SPORTS MOLE SAYS: Rochdale 0-3 Tottenham
This will be the first ever competitive clash between Rochdale and Tottenham in any competition, so both teams are facing slightly unknown quantities this afternoon.
Indeed, Spurs have not been beaten by a third-tier side since January 1988, when they lost to Port Vale, which helps to give some context to the size of the task in front of Rochdale this afternoon.
It is now 10 years since Spurs last lifted silverware and 17 since they won the FA Cup, so a trophy is long overdue. Pochettino will also be keen to pick up his first piece of silverware as manager, if only to show a tangible reward for the team's undoubted progress under him.
ROCHDALE STARTING XI: Lillis; McGahey, McNulty, Delaney; Rafferty, Cannon, Camps, Kitching, Done; Henderson, Humphrys
TOTTENHAM STARTING XI: Vorm; Trippier, Alderweireld, Foyth, Rose; Wanyama, Winks, Sissoko, Lucas, Son; Llorente
It is another really good team move from the hosts as Winks gives the ball away and Rochdale immediately pour forward on the counter. Cannon is in acres of space and produces the quality needed with the final pass to release Henderson. He has missed two good chances already today, but there is no doubt about this one as he slides his finish past Vorm from inside the area.
Rochdale are well worth their lead too, having created a number of good chances and more than held their own against the might of Tottenham. We are in for a very interesting second half!
Ian Henderson had missed two good chances prior to the opener, but he made no mistake when a third opportunity came his way following a slick team move from the hosts. A counter-attack sliced right through Spurs and Henderson collected the ball inside the area before slotting his finish past Vorm.
As mentioned, Henderson has squandered the two best chances aside from the goal, with the Rochdale top scorer firing one into the arms of Vorm and slicing another horribly off target.
Pochettino made a full 11 changes from the midweek draw at Juventus, but it may not be too much longer before he looks to bring on some of the big guns in an effort to rescue this one.
Sissoko slides a pass through to Lucas, who has managed to escape the attentions of the defence on the edge of the box. The winger takes it in his path and strokes his finish past Lillis as the keeper was coming racing off his line.
18 - Lucas Moura has been directly involved in 18 goals (12 goals, six assists) in his last 20 starts in all competitions for both Tottenham and PSG. Dazzling.— OptaJoe (@OptaJoe) February 18, 2018
Alli is upended inside the area and Bobby Madley is quick to point to the spot. Kane steps up and tucks a brilliant penalty into the bottom corner, leaving the keeper no chance despite him guessing the right way.
The ball breaks to Davies in the area and he takes a touch before tucking his finish away with aplomb, leaving Vorm no chance! The home crowd erupt!
The League One strugglers really began to tire in the second half and looked to have lost it when Harry Kane tucked home an 88th-minute penalty, after Lucas Moura had earlier marked his full debut by cancelling out Henderson's surprise opener.
However, Steve Davies had the final say with a 92nd-minute equaliser which sets up a replay at Wembley.
Thank you very much for joining Sports Mole for today's match as Rochdale stun Tottenham at the death to earn a replay at Wembley and keep their quarter-final dreams alive. I will leave you with our match report, and be sure to stick around for reaction too.
From me, though, it is goodbye for now!