It had been nip and tuck for the first 50 minutes, with Slade claiming Yeovil had looked the better side. But when their skipper departed, again troubled by a persistent groin injury, their defence never looked the same.
In the first half Paul Warne looked dangerous for Yeovil and came close to scoring in the fifth minute when he burst through on the left and fired across the face of the goal.
Marcus Stewart was also off-target, while at the other end there was little to trouble Romain Larrieu, the goalkeeper on loan from Plymouth Argyle.
Forest, beginning to blossom after a shaky start to the season, grabbed the vital opening goal on 57 minutes. Richie Jones conceded a free-kick on the left.
Sammy Clingan floated it towards the box and Kevin Wilson's header was knocked in from close range by Luke Chambers.
Little had been seen of last week's Forest hat-trick hero Junior Agogo but he emerged from the doldrums on 62 minutes to bring a brilliant save from Larrieu and in the 79th minute he added the second goal with a fine piece of opportunism.
The big striker charged down Scott Guyett's clearance and with the goalkeeper off his line hammered a 35-yard drive into the roof of the net.
Yeovil's misery was complete in the 84th minute when Grant Holt fed a precision pass to substitute Kris Commons and he lobbed Larrieu and his effort went in off the underside of the bar.