The Wanderers' qualification to the third round never looked in doubt throughout the 90 minutes. After a commanding first-half performance, Wolves made their quality tell just before the hour mark when Romain Saiss tapped in the back post from a Joao Moutinho cross.
On his return to action, Daniel Podence doubled the visitors lead minutes later after the winger picked up the ball from Fabio Silva's cross before calmly sliding the ball into the bottom corner.
Another two goals in close proximity came in the closing stages through Francisco Trincao and Morgan Gibbs-White. Trincao's first goal for the club came after some sensational one-touch football on the edge of the area before Silva slid the ball into the box for Trincao to finish whilst Gibbs-White struck the ball into the bottom corner after a brilliant solo run.
With just over 50 hours since Wolves' Premier League defeat to Tottenham Hotspur, Bruno Lage made seven changes- handing Daniel Podence his first piece of action since the 2-1 victory over Brighton & Hove Albion in May.
John Ruddy, Ki-Jana Hoever, Rayan Ait-Nouri, Leander Dendoncker, Morgan Gibbs-White and Fabio Silva joined Podence in the starting 11, with Raul Jimenez, Ruben Neves and Adama Traore on the bench.
The home side rang the changes themselves from Saturday's 1-0 defeat to Stoke City. Teenager Fin Back the only survivor in Chris Hughton's squad.
After only five minutes Wolves created their first chance of the evening through Podence. Ait-Nouri's trickery saw him beat Back before the French wing-backs cross eventually made its way to Podence 12 yards out. Despite not seeing it until later, former Club Brugge goalkeeper Ethan Horvath reacted well to keep the scores level.
Podence was presented with another great opportunity to score moments later when Joao Moutinho's lovely dinked pass was too much for Baba Fernandes to leave only Horvath to beat. After attempting to round the goalkeeper, Podence attempted a backheel and the American goalkeeper read it perfectly to send the ball wide.
Forest registered their first attack of the game shortly after 15 minutes. A floated free-kick into the Wolves penalty area by Jack Colback fell to the feet of Lewis Grabban, whose shot from close range was blocked by Romain Saiss.
Podence's impact was beginning to show and he had another great chance to score after 20 minutes. The winger danced his way through the Forest defence before firing the ball across goal and smashing the post before the ball landed directly in Horvath's grasp.
Wolves ended the half with 12 shots (five on target) with over 70% possession. Their Premier League experience and quality was clear but, like their previous two games, the finishing touch was missing.
The home side came out in the second half with more threat and intensity and managed to muster a great chance themselves. Following a failed clearance from Wolves, Ateef Konate's deep cross found Oliver Hammond at the back post but the 18-year-old headed wide.
Wolves' dominance and persistence finally paid off before the hour mark with two quickfire strikes. The opener came from Saiss after a short corner routine was eventually put into the box for the Moroccan defender to stick his leg out and score.
It was 2-0 almost immediately after when Forest gave the ball away in the middle of the park and allowed Silva the freedom of the city on the right-hand side. The striker managed to slash the ball across goal for Podence to check inside before simply slotting the ball past Horvath.
Wolves continued to press their opponents and Forest were lucky remain in the game. However, the final nails in the coffin were dealt through goals by Trincao and Gibbs-White.
Trincao's first goal for the club came after some sensational play on the edge of the area before the Barcelona-loanee tucked the ball away.
Not long after and it was four when Gibbs-White picked the ball up on the halfway line, drove towards goal before unleashing a impressive strike past Horvath.