The French defender marked his first start for us at centre-back with his second goal in a Spurs shirt - heading home Reto Ziegler's inswinging corner in the 59th minute.
Twelve minutes later and Keane was there to provide the finishing touch to a carbon-copy goal as Michael Brown flicked on Ziegler's corner to continue his run in the competition after earlier goals against Brighton and West Brom.
Substitute Mido completed the scoring in injury time after Michael Brown's shot crashed off the underside of the crossbar.
It was another stern test for us against Gary Megson's men although Forest didn't provide the same threat in attack as they did in the 1-1 draw at the Lane. Kris Commons was a big miss for them as Gareth Taylor and David Johnson failed to dent the new-look centre-back pairing of Pamarot and Anthony Gardner.
They were two of seven changes to the side that beat Fulham in the Barclays Premiership on Saturday with Thimothee Atouba, Pedro Mendes, Reto Ziegler, Robbie Keane and Fredi Kanoute also in for Erik Edman, Michael Carrick, Andy Reid, Mido and Jermain Defoe respectively.
We just about had the upper hand in a scrappy first half. Not too much happened in terms of goalmouth action - Kanoute and Robertson sliced a shot each wide - until Keane had two chances in a matter of seconds on the half-hour mark.
The first came after the best move of the half as Atouba and Ziegler worked their way up the left, Atouba clipped ball into Kanoute who chested down for Keane to hit from 10 yards but Gerrard was down smartly to his right to palm out.
As play continued, Davies knocked the ball back in, Forest waited for an offside flag that never came and this time Keane failed to connect from close range.
Ziegler cracked a volley just wide, Atouba and Mendes were wat off target from distance and then Forest's best chance just a minute before the break, Robertson latching onto a loose ball and forcing Robinson to parry to his left.
The second half followed a similar pattern with us on top in terms of possession but Forest, starting again with three central defenders, holding firm at the back.
We finally broke through via a set-piece routine after 59 minutes. Pamarot darted across the near post and Ziegler's delivery from the corner was perfect to flick home with Gerrard flapping.
The goal seemed to deflate the home side as we went in search of a second goal.
Gerrard was forced to save from Ziegler and Keane within a minute but he could do little to prevent Keane tapping home for 2-0 after 71 minutes. Ziegler's corner was perfect again, Brown flicked on and the Irish star did the rest from close range.
That was just about it although Gerrard denied Keane again four minutes from time and James Perch volleyed Forest's best chance wide before Mido nodded home the third after Brown's 25-yarder came back off the underside of the crossbar.
GUIDE TO THE ACTION
13mins: Brown led break from a Forest corner, linked well with Davies but Melville there to cut out cross.
19mins: First chance of note, Atouba picked out Kanoute's run behind Forest defence, tight angle, Kanoute sliced shot wide.
21mins: Melville flicked header from Evans corner deflected just wide with Robinson under pressure.
25mins: Curtis cross landed over Johnson and Kelly, Robertson following late made hash of attempted shot.
30mins: SAVE. Best move so far, Atouba and Ziegler involved, Atouba clipped ball into Kanoute who chested down for Keane to hit from 10 yards, Gerrard down smartly to his right to palm out.
30mins: MISS. Davies played ball in from right, Forest waited for offside, no flag, Keane failed to connect with left foot six yards out.
34mins: Mendes sliced wide from 25 yards.
42mins: Corner routine, Davies chipped it to the edge of the box where Ziegler cracked volley wide.
43mins: Atouba smashed shot into the stand from 28 yards.
44mins: SAVE. Ball played into box, half-cleared, Evans worked a yard 18 yards out and hit shot that forced Robinson to parry to his left.
Half-time: Forest 0, Spurs 0
52mins: First shot of half, Kelly early ball from right hit first time by Kanoute straight at Gerrard who almost spilled it for Keane following in.
56mins: YELLOW. Melville for foul on Keane.
57mins: Melville great block to deny Kelly, onto loose ball as Kanoute's free-kick bobbled around the box.
59mins: GOAL. After spell of pressure and couple of free-kicks, Pamarot glancing near post header from Ziegler's inswinging corner.
Forest 0, Spurs 1
63mins: SUB. Thompson for Evans.
66mins: SUB. Harris for Johnson.
69mins: CHANCE. Ziegler break from Forest attack, had support but opted to shoot, decent save by Gerrard.
70mins: SAVE. Gerrard forced into acton again, this time to block Keane snapshot from 18 yards.
71mins: GOAL. Another Ziegler inswinging free-kick this time flicked on by Brown at near post and finished by Keane from close range.
Forest 0, Spurs 2
72mins: SUB. Mido for Kanoute.
76mins: Carrick for Mendes.
80mins: SUB. Edman for Atouba.
86mins: SAVE. Keane through on Gerrard who spread himself well to block.
88mins: MISS. Forest's best chance of night, Doig deep cross volleyed wide by Perch at far post.
90mins: GOAL. Mido headed home the rebound after Michael Brown's shot crashed against the underside of the crossbar.
Forest 0, Spurs 3
Full-time: Forest 0, Spurs 3
Nottingham Forest: Gerrard, Morgan, Powell, Evans (Thompson, 63), Johnson (Harris, 66), Taylor, Doig, Curtis, Robertson, Perch, Melville. Subs: Doyle, King, Bopp.
Spurs (4-4-2): Robinson, Kelly, Atouba (Edman, 80), Gardner, Pamarot; Davies, Mendes (Carrick, 76), Brown, Ziegler; Keane, Kanoute (Mido, 72). Subs: Cerny, Defoe.
Robbie Keane maintained his record of scoring in every round of this season's FA Cup but Noe Pamarot made the crucial breakthrough in Wednesday's fifth round replay win at the City Ground.