The young winger scored with a sumptuous curling effort to give The Reds an early lead which was cancelled out almost immediately by a heavily deflected Aron Gunnarsson effort.
Substitute Nelson Oliveira could have won the game for Forest with the last kick of the match but he blazed the ball over from six yards after David Marshall parried a shot in the forward's direction.
Dougie Freedman made six changes to the team that drew with Leeds two days ago. Oliver Burke, Jamie Ward, Jonny Williams, Robert Tesche, Liam Trotter and Dexter Blackstock came in and Henri Lansbury, Ryan Mendes, Nelson Oliveira, Chris O'Grady and Osborn dropped to the bench.
Cardiff claimed the first chance of the match on five minutes when Craig Noone's deep cross was headed back across goal by fellow winger Anthony Pilkington. The ball bounced inches wide of the far post as Forest received an early let-off.
The home side were hit with a sucker punch on ten minutes however. Tesche broke up play in midfield, allowing Blackstock the chance to supply Oliver Burke down the right. The youngster cut inside in the area and bent the ball towards the far corner with the outside of his boot. The ball nestled in the net to give the winger his first senior goal.
But Forest had the lead for only three minutes. Gunnarsson received the ball 22 yards out and struck it low towards goal. It took a huge deflection off Tesche, wrong-footing de Vries, and sailed into the net.
Seconds after play resumed, Tesche nearly sent the ball into the opposite net when it bounced kindly for him just outside the area. The German lashed it just wide.
It was proving to be an end-to-end affair and on 15 minutes Noone beat Michael Mancienne down the right and hung the ball up for Pilkington at the back post once again. This time Pilkington got his header on target but Dorus de Vries was untroubled.
The Dutch stopper was called in to make another comfortable save on 24 minutes, denying Joe Ralls, before he was forced to make a much more impressive stop a minute later. The ball ran through for Tony Watt in the area and de Vries got down brilliantly at his near post to prevent the Bluebirds taking the lead.
Oliver Burke was providing flashes of excitement for Forest and he could have doubled his goalscoring tally on the half-hour. Eric Lichaj's strong run down the right resulted in him cutting the ball back for the youngster in the area. Burke took it first time but couldn't keep his shot down.
Blackstock was the next Forest player to be left frustrated as the first half entered its latter stages. Cardiff keeper David Marshall got a fingertip to Ward's dangerous cross and the ball just evaded Blackstock, who for a moment looked like he would have a tap-in at the back post.
The second half began with a similar chance for Forest as Blackstock made a nuisance of himself as he tried to latch on to Tesche's dinked free-kick. The ball dropped near Williams six yards out but the attacking midfielder was unable to pounce and Marshall claimed.
Gunnarsson could have had his second of the night after a Cardiff free-kick was blocked by Forest's wall. Noone picked up the pieces and dinked the ball into the middle, where Gunnarsson rose highest. The Icelander could only head it harmlessly wide.
Freedman made his first change on 71 minutes, sending on Osborn in place of Williams.
And the substitute nearly played a huge role in putting Forest ahead with 11 minutes to play. Tesche and Ward exchanged passes in the middle before releasing Osborn down the right. The wide midfielder drilled the ball low into the centre where Ward was able to make contact, but he couldn't turn it home from just outside the six-yard box.
Oliveira was the next Forest player to be introduced, replacing Blackstock, before Lansbury came on for Burke with five minutes of normal time remaining.
A further five minutes were added on at the end of the match and Oliveira had a golden opportunity to win it in the dying seconds. Marshall could only parry Lansbury's effort towards the Portuguese forward six yards out but, with the ball bouncing, Oliveira sent it high over the bar.
Forest: De Vries, Lichaj, Mills (c), Hobbs, Mancienne, Ward, Trotter, Williams (Osborn 71'), Tesche, O.Burke (Lansbury 85'), Blackstock (Oliveira 80')
Sub not used: Evtimov, Mendes, C.Burke, O'Grady
Goal: O.Burke 9'
Booking: Ward 77'
: Marshall (c), Peltier, Manga, Connolly, Fabio, Noone (Cardiff
Macheda 81'), Gunnarsson (Whittingham 70'), Ralls, Pilkington, Watt, Jones (Ameobi 65')
Subs not used: Moore, Malone, O'Keefe, Mason
Goal: Gunnarsson 13'
Booking: Fabio 87'
Referee: Tim Robinson
Attendance: 15,461 (859 away)