The Dale, currently battling relegation in League One, will travel to St James’ Park for a replay, thanks to a spirited display which saw them equalise 11 minutes from time.
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Stephen Humphrys ensured that Rochdale were 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.
In the reverse fixture, Spurs needed a late Harry Kane goal to rescue a 1-1 draw