Goals from midfielders David Morgan and Ben Osborn either side of the break ensured victory in a game The Reds dominated.
The first chance fell to Coventry on 2 minutes as Will Roberts ran clear but could only fire wide.
Forest responded immediately but Nabil Guedioura saw his lob float over Lee Burge's goal.
On seven minutes, The Sky Blues' Louis Garner fired just wide from the edge of the area.
Shortly after, Morgan Ferrier linked up well with Osborn who found Guedioura at the near post, but the striker's first-time effort went just wide.
In the 13th minute, David Papworth showed good anticipation to win possession before Guedioura set up Morgan, but the midfielder's long-range effort went over.
The home side almost took the lead on 20 minutes after a marauding run by captain, and centre back, Nathan Cameron got him into Forest area, but his shot was saved well by Dimitar Evtimov.
On 22 minutes The Reds had a chance of their own. More good work by Ferrier in the left channel set up Morgan but he couldn't control his finish.
The visitors then had two chances in quick succession. Firstly, Ferrier's close-range shot was blocked by Kevin Malaga and then Guedioura's long-range effort was saved low by Burge. Ferrier was in amongst it again a minute later but couldn't quite escape the attentions of Malaga as he ran through on goal.
The deadlock was finally broken on 31 minutes when Morgan burst from midfield to finish well beyond Burge.
It was almost 2-0 moments later when Osborn almost found Guedioura at the front post but the Algerian couldn't quite make contact.
And just before the break a looping shot from Jack Blake couldn't beat Burge. After the break, the referee denied Forest a penalty when he turned a blind eye to Burge's trip on Guedioura.
On 53 minutes, Papworth rounded off a good spell of possession with a clean strike at goal but Burge was equal to it.
More impressive passing led to a speculative effort from Morgan 5 minutes later but it wasn't enough to double his tally.
The lead was extended on 71 minutes, however, after a stunning left-footed strike by Osborn. Ferrier held the ball up on the edge of the area before laying off to the left winger, who connected beautifully to send a rocket into the top corner.
Forest U21s: Evtimov; Andrews, Regan, Fenton, Gregory (trialist); Osborn, Blake, Morgan (Gorman), Papworth (G'Nahore); Ferrier, Guedioura (Palmer-Samuels).