Keinan Davis pulled one back in the fourth minute of added time at the end of the second half, but it was too little, too late for Forest.
The result puts Cardiff 20th in the table, six points clear of the drop zone while Forest stay eighth, two points outside of the play-off places.
Story of the match
Cardiff started the game brightly and were rewarded on five minutes when Perry Ng won the ball back in midfield and played a superb pass through to debutant Jordan Hugill who raced through on goal and found the bottom left corner with his sidefooted effort.
The visitors began to dominate the ball after the opening goal and were nearly level ten minutes later when Djed Spence crossed from the right to find Jack Colback who was put off by Tommy Doyle and saw his effort go wide of the post.
Forest came close to an equaliser ten minutes later when Spence and Brennan Johnson linked up down the right, Johnson fizzed a ball across the face of goal which after a poor clearance from Cody Drameh, was punched away from danger by City goalkeeper Alex Smithies.
The Bluebirds almost doubled their lead just after the half-hour mark when midfielder Joe Ralls spotted Forest keeper Brice Samba out of position, his half volley was just wide of the Forest post.
Steve Morison's side came close again just minutes later when a dangerous cross from Drameh on the left found Hugill whose first-time volley was saved well by Samba.
The final ten minutes of the first half offered little goalmouth action and it was Cardiff who were ahead at the break.
Forest started the second half looking shaky and almost handed Cardiff their second when Samba misjudged a poor back-pass from Scott McKenna, luckily for Samba the pass went just wide of the left-hand post.
McKenna nearly made another error from the resulting corner when he brought down Sean Morrison in the Forest penalty area, an incident which was missed by the officials.
Steve Cooper's side did almost equalise moments later when a good attacking run from Ryan Yates allowed him to play a low pass into the six-yard box where Ng was on hand for Cardiff to clear the danger.
The visitors were inches away from an equaliser five minutes later following some neat play from James Garner who fired a ball across the face of goal which was just beyond Johnson who came sliding in but couldn't get any contact on the ball for what would have been a tap in.
Substitute Isaak Davies made an instant impact for Cardiff just before the hour mark when he put in a cross from the right which found Hugill whose shot was blocked well after a desperate challenge from Steve Cook.
Davies made an even bigger impact just five minutes later when he scored Cardiff's second goal of the game, a sensational, curling Joe Ralls strike from range rattled the Forest post and Davies was in the right place at the right time to tap home into an empty net and double the Bluebirds’ lead.
Forest should have pulled one back 20 minutes from time when the ball fell to Spence in the box who, with plenty of time, blasted his effort into the stands.
Substitute James Collins came on for the hosts and looked as threatening as the man he replaced, Jordan Hugill, when he got on the end of a curling Ralls cross and headed over.
The visitors should have set up an exciting final five minutes when substitute Xande Silva had a golden opportunity to pull one back, his effort had too much on it and went over the bar.
The visitors pulled one back in the fourth minute of added time when Keinan Davis headed in from a corner to make it a nervous final few minutes for Cardiff.
However, it was too little, too late for Forest and Cardiff saw out the win.
Takeaways from the game
Hugill and Watters
Cardiff fans will be travelling home from the Cardiff City Stadium delighted with the partnership Jordan Hugill and Max Watters look to have formed up top.
Morison seems to have found a winning combination that could prove vital in the Bluebirds’ survival this season.
Hugill's physical presence and excellent ability to hold up the ball was clear for all to see on Sunday afternoon and alongside Watters who stretched the Forest defence with his pace and movement as they looked as though they had found a balance that looks dangerous.
Set piece danger
Both sides had contrasting styles in the game with Cardiff using the huge physical presence in their side to look dangerous in the air, particularly from set-pieces.
The Welsh side gave the Forest defence plenty to think about from dead ball situations on Sunday and will hope to become the Championship's set-piece specialists in their bid for survival.
There is only one man who comes to mind when picking the stand-out player from the match: Jordan Hugill.
Hugill signed on loan from Norwich City on the morning of the game and his debut goal on five minutes set the Bluebirds on their way to victory.
The striker gave the Forest defence a tough 70 minutes before he was substituted off and ticked all the boxes for Steve Morison's side.
If Hugill can perform as he did on Sunday for the rest of the season, Cardiff will have a fantastic chance at survival in the second tier this seaosn.