The Reds wasted little time in making their intentions clear as they raced into a 3-1 lead before half-time, courtesy of goals from Julian Bennett, Kris Commons and Lewis McGugan.
Bennett set the ball rolling as he fired Forest in front after just 12 minutes, curling home a left-footed shot from outside the area.
Commons doubled Forest's lead five minutes later as he fired through goalkeeper Steve Mildenhall's legs after being sent clear by Nathan Tyson.
Yeovil dampened the party atmosphere by pulling one back just two minutes later, with Jaime Peters firing home after playing a neat one-two with strike partner Marcus Stewart.
But McGugan's superbly-executed 27th-minute free-kick restored Forest's two-goal lead, before Yeovil added to Forest's nerves 17 minutes from time when substitute Andy Kirk headed home from Marc Bircham's cross.