Forest gave a rare start to striker David Johnson, while Spurs boss Martin Jol opted to pair Robbie Keane and Fredi Kanoute in attack, leaving Jermain Defoe and Mido on the bench.
The early minutes saw few chances for either side, with both teams struggling to come to terms with a bobbly playing surface.
Midway through the first period Gregor Robertson lashed a shot well wide of target for the home side, as neither goalkeeper was brought into serious action.
Keane then had two chances inside a minute, firstly being denied by an excellent save from Paul Gerrard before scuffing the second effort straight at the keeper from 12 yards.
Reto Ziegler was well off-target with a drive from the edge of the area five minutes before the interval, while Paul Evans brought a first save from Paul Robinson at the other end.
After the restart, Spurs began to up the pace but still gave Gerrard little work to do.
Shortly before the hour a Kanoute free-kick from the edge of the area caused panic in the Forest box, but the home side cleared the danger.
However, there was to be no escape soon after as Ziegler's inswinging corner from the right was flicked home at the near post by Noe Pamarot.
Twenty minutes from time Ziegler should have doubled the lead after a quick counter-attack, the Swiss forcing a save from Gerrard with two team-mates looking for a pass.
Keane made no mistake within two minutes as another Ziegler corner was flicked on by Michael Brown to the far post and the Irishman netted from almost on the goal-line.
The closing minutes saw Forest unable to force their way back into the game, as Spurs clinched a sixth round spot with some ease - Keane almost adding a third, being denied by an excellent Gerrard save.
The Premiership side did make the final score 3-0 in stoppage time as Brown's 25-yard shot hit the crossbar and sub Mido was on hand to nod home the rebound.