Gary Hooper and Marco Matias' second-half strikes added to Aiden McGeady's 30th-minute effort in a match which also saw Wednesday's Barry Bannan sent off late on.
Dougie Freedman made two changes to the side that beat Preston. Nelson Oliveira, who hobbled off in Tuesday's second half with a groin strain, made way for attacking midfielder Jorge Grant, while Robert Tesche was replaced by David Vaughan.
Oliver Burke made a welcome return to the squad, joining fellow youngsters Tyler Walker and Gerry McDonagh on a bench which also included experienced campaigners Tesche, Bojan Jokic and Kelvin Wilson.
Forest, kicking towards the Trent End, made the stronger start and had the first chance of the game on five minutes. Ben Osborn supplied Vaughan on his weaker right foot but the Welshman's shot from 25 yards was comfortably saved low down by Keiran Westwood.
The Reds carved out another opening four minutes later following good wingplay by Ryan Mendes. The Cape Verdean's low cross was toe-poked into Grant's path by Chris O'Grady but the youngster was always stretching to take the shot, sending the ball high and wide from 20 yards.
Wednesday were boosted by the return from suspension of top scorer Fernando Forestieri, who had his first sight at goal on 11 minutes when he received the ball on the edge of the area. His powerful strike was parried by Dorus de Vries but Forest failed to clear, presenting the ball back to the Italian. De Vries was equal to his second effort, however, smothering the danger.
Chris Cohen isn't a player known for his goalscoring exploits but when Wednesday afforded him plenty of time and space after he had moved forward from left back, he couldn't resist a shot. The ball flicked off Liam Palmer, momentarily wrong-footing Westwood, but the keeper managed to readjust his position in time to make the save.
It was proving to be an end-to-end opening to the match and Forest had to rely on an excellent sliding block by captain Matt Mills to keep the scores level on 24 minutes. Gary Hooper flicked the ball into Kieran Lee's path in the area and the defender had to slide in at the near post to divert it behind.
But the Owls were ahead shortly afterwards. Bannan's sliderule pass made life difficult for Eric Lichaj, who couldn't sort his feet before McGeady nipped around him, composed himself and smashed the ball past de Vries.
The visitors thought they had a second shortly afterwards when Bannan's beautifully-struck volley following a half-cleared corner saw the ball flash through a crowd of bodies and into de Vries' grasp.
Forest could easily have been level with half-time approaching, however, as a corner of their own caused problems in the Wednesday box. The ball came all the way out to Osborn at the back post, who whipped it back into the middle with pace. Grant guided the ball goalwards with a glancing header but could only direct it straight at Westwood.
The end-to-end nature of the half meant Wednesday would claim the last chance before the break and it fell to danger man Forestieri. Vaughan's miscued pass presented the ball to McGeady 25 yards out. His strike was scuffed but, somewhat fortuitously, the ball skidded into the feet of Forestieri ten yards out. His control was instant but his finish not quite as clinical, de Vries getting down to his left to make the stop.
Neither manager made changes at the break and Forest came back out of the blocks quickly. Lichaj took the ball forward before floating it towards Osborn on the edge of the area. The midfielder knocked it down for Grant, who let the ball bounce to give himself time to take the shot on his right. He could only send the ball dipping over the bar, however.
That was to be Grant's final action as Freedman replaced him with Burke on 56 minutes.
But Forest, missing so many of their creative players, were struggling to build any attacking momentum - and their limited options proved to be their downfall on 62 minutes. Mills, forced to patiently weigh up his options in possession, was robbed by Forestieri who rolled the ball to Hooper for a simple finish.
Cohen conjured Forest's response, seeing his powerful strike pushed behind by Westwood, before Tesche replaced Gardner in central midfield.
The Reds were still struggling to properly trouble the visitors, however, and nearly found themselves 3-0 behind when Bannan's free-kick from a wide position saw the ball flash just wide of the far post.
Burke, who has recently received his first call-up to the Scotland senior team, provided some incisiveness shortly afterwards. He burst away down the right and floated the ball into the middle, where O'Grady was unable to make proper contact with his header. The ball came to Mendes who, from a tight angle, saw his shot pushed wide by Westwood.
Forest's cause was helped on 76 minutes when Bannan was shown a straight red card for a high foot on Lichaj, which left the full back needing treatment.
Freedman's final change saw Walker replace Cohen with eight minutes remaining, but there was nothing the forward could do to prevent Wednesday from extending their lead when two substitutes combined. Atdhe Nuhiu's knock-down allowed Matias to work a shooting opportunity in the area before stroking the ball into the far corner of the net.
Five minutes were added on at the end of the match but Forest were unable to find a goal.
Forest: De Vries, Lichaj, Mills (c), Mancienne, Cohen (Walker 82'), Mendes, Gardner (Tesche 66'), Vaughan, Osborn, Grant (O.Burke 56'), O'Grady
Subs not used: Evtimov, Jokic, Wilson, McDonagh
: Sheffield Wednesday
Westwood, Palmer, Loovens, Lees, Pudil, McGeady (Matias 73'), Bannan, Lee, Wallace (Lopez 67'), Forestieri, Hooper (Nuhiu 79')
Subs not used: Price, Hunt, Turner, Joao
Goals: McGeady 30', Hooper 62', Matias 85'
Sent off: Bannan 77'
Referee: Graham Scott
Attendance: 20,690 (1,841 away)