Tottenham were caught on the counter-attack when Rochdale struck first as a controversially relaid pitch at Spotland Stadium proved conducive to passing football.
Up front, new boy Lucas Moura made his first start for the club after his late cameo in Italy in midweek.
Rochdale, bottom of League One, can now look forward to a money-spinning replay at Tottenham's temporary Wembley home. "The good news is that we are still alive and we have the possibility to play again at Wembley".
It is another game for Spurs, one they don't need, but for Dale's players and their supporters, it will be the stuff of dreams when the rematch takes place later this month.
Rochdale are now not in their best of form with their ultimate aim being to avoid relegation from the League One at the end of the season.
West Bromwich Albion's tumultuous week took a final turn for the worse as they were knocked out by Southampton, whose 2-1 victory at the Hawthorns secured the visitors a quarter-final berth for the first time since 2005.
Having missed a great chance to put his side ahead earlier on, volleying wildly after a great pass from Callum Camps, the 33-year-old scored his 15th goal of the season and his sixth in this year's FA Cup campaign.
"My comment was about the care, first of all for the Rochdale players, our players and the competition that all of England watches on TV".
After a trophyless period since his appointment at Spurs, Mauricio Pochettino knows well the importance of the FA Cup and is very much in contention to win it, if his team could replicate the recent form till the end of the season. In an instant Hill's team were on the counterattack and Cannon fired the flawless pass behind the visiting defence for the former Norwich City forward, who nearly quit the game to study dentistry five years ago, to sidefoot a superb first-time finish into the bottom corner. The Latics attention will temporarily turn away from the chase for promotion and to the FA Cup.
"Because the game isn't just about finishing third, fourth or fifth and being a great team to watch - you have to be winning trophies", former England global Stan Collymore writes.