Goals from Nicolao Dumitru-Cardoso, Gboly Ariyibi, Toby Edser and Anel Ahmedhodzic sealed all three points on a positive afternoon for The Reds as both Chris Cohen and Armand Traore played over 70 minutes on their return from injury.
The only sour note for Forest was an arm injury sustained by Hildeberto Pereira in the second half as the midfielder left the field on oxygen and with his arm in a makeshift sling following a challenge by Brad Maslen-Jones.
Both sides had good goalscoring opportunities early on as Ariyibi's low shot was well held by City goalkeeper Jonathan Saltmer before Will Annan headed wide for the visitors from a dangerous right-wing cross by James Yates.
Joao Teixeira then narrowly cleared the crossbar with a dipping long-range volley before Dumitru dragged a shot into the ground when well-placed inside the penalty area but the striker did make the breakthrough on 32 minutes.
Pereira picked the ball up 20 yards from goal and delivered a smart reverse pass into Dumitru's path and he produced a composed, low finish beyond Saltmer and into the far corner of the Hull net.
Forest doubled their advantage in the final minute of the first half as Ariyibi was able to find a yard of space inside the penalty area and he sent a curling shot past Saltmer to give The Reds a commanding lead at the break.
There were 63 minutes on the clock when Pereira had to be taken from the field. The midfielder was hacked down by Maslen-Jones on the touchline as he led a counter-attack and after spending a few minutes receiving treatment, he was replaced by James Thorne.
Forest weren't to be distracted from their task though and extended their lead two minutes later. Cohen's ball out wide found Dumitru in space, the striker made a run for the byline and pulled the ball back for Edser to side-foot home.
The visitors hadn't provided much in the way of an attacking threat but Jordan Wright did have to be alert to prevent them from finding the net. Johan Ter Horst broke in behind the back four and raced towards goal but Wright stood firm to make a good close-range stop.
With five minutes remaining, Forest put gloss on the scoreline and sealed their victory. A bouncing ball inside the City penalty area wasn't dealt with and Ahmedhodzic was on hand to loop a header past Saltmer and into the net.
The result will give Gareth Holmes's side some much-needed confidence ahead of their Premier League Cup meeting with Leicester City at Alfreton Town on Friday night (kick-off 7pm).
Forest: J.Wright, Charlesworth, Ahmedhodzic, Iacovitti, Traore (Crookes 74'), Ariyibi, Edser (c), Cohen (Otim 77'), Pereira (Thorne 63'), Teixeira, Dumitru-Cardoso
Subs not used: Marques, Gomis
Hull: Saltmer, Yates, Fleming (Maslen-Jones 11'), Batty, Barkworth, Thacker, Annan (c), Kelledy (Chadwick 75'), Ter Horst, Lofts, Hinchliffe
Subs not used: Andrew, Sheaf, Salam