Calvin Andrew headed home a second-half winner for his third of the season to make it a league and cup double for the crisis-hit Hatters over Colin Calderwood's men.
The Kenilworth Road outfit, plunged into administration for the third time in eight years earlier in the month, will now have a money-spinning live Sky clash with the Reds to look forward to on Sunday, January 6.
The last time the sides met the teams played out a classic encounter that was eventually won 5-3 by the Merseysiders.
In icy conditions both sides took a time to warm to the task at hand as David Bell fired an ambitious, angled drive at Paul Smith from 20 yards in the seventh minute before James Perch nodded wide from Chris Cohen's corner six minutes later.
The temperature soon rose though as the Hatters twice went close in the space of seconds in the 19th minute.
Darren Currie's clever corner allowed Matthew Spring to send in a diving header from just inside the penalty area that deflected off Bell before being cleared off the line by Kelvin Wilson.
From the rebound, Spring was first to the loose ball, but could only pull his left-foot shot wide from 12 yards with Dave Edwards just failing to convert at the far post.
Currie sent a rasping left-foot drive just past the post from 30 yards in the 26th minute before Bell collected a kick from goalkeeper Dean Brill and cut inside from the right flank, before hitting a 20-yard shot that was tipped aside by Smith.
Bell was involved again in the 37th minute as he raced on to Steve Robinson's pass and crossed for Currie on the opposite side of the penalty area, who in turn pulled back for Andrew to see a 15-yard shot saved by Smith.
Luton kept attacking after the break and finally broke the deadlock in the 54th minute when Currie over-hit his corner, only for Spring to hook the ball back into the danger area for Andrew to rise highest in the six-yard box and glance the ball home.
Matt Lockwood saw an 18-yard effort well saved by Brill just after the hour.
But the hosts almost extended their lead in the 64th minute when Andrew crossed from the left for Edwards to hit an instant volley from 12 yards, only for Smith to claw the ball away at full stretch.
Forest made a double substitution in the 71st minute as Junior Agogo replaced Nathan Tyson and Kris Commons came on for Lewis McGugan.
And two minutes later they almost had an equaliser as Perch fed Chris Cohen, who raced clear and slipped the ball past Brill, only for Chris Perry to hack the ball to safety.