Matt Done and Mark Kitching stood out early on, while the home fans appealed vociferously for a penalty when Andrew Cannon harried Toby Alderweireld and the defender appeared to handle the ball on the ground.
Llorente struggled to impose himself on the game and was replaced by Harry Kane to provide Spurs with a threat in front of goal.
In the 59th minute, Moura netted a vital equaliser - his first goal for the club on his first start.
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.
Office hazards: Women working as cleaners face increased lung function decline
The men who cleaned, in the meantime, did not experience greater decline in the exhale tests than those who did not clean. The accelerated lung decline was "comparable to smoking somewhat less than 20 pack-years", they conclude.
GK Michel Vorm, 6 - Beaten twice but can not really be blamed for either goal, and he stuck to Pochettino's principles in passing the ball out, even when things were not going to plan in front of him. Son Heung-Min could also start, and Pochettino will be hoping he plays a starring role in the absence of fellow regulars.
Rochdale took umbrage at claims they were giving away an advantage by relaying the pitch, and set about showing they, too, prefer a surface conducive to passing.
Kane, who made his Football League debut at Rochdale for Leyton Orient in 2011, happily signed autographs and posed for pictures before kick-off.
The second-half brought much of the same for Spurs, a few good chances however, no real threat to a resilient Rochdale.
One big positive was that I rewlly enjoyed Lucas. Newport gave us a fantastic game and they lost their next game in the league 5-0.