That result ended Fulham's 23-match unbeaten run in the Championship and forced them to settle for a playoff spot.
Cardiff finished with 90 points, two points ahead of Fulham but nine adrift of champions Wolverhampton Wanderers.
"It's the biggest achievement in my 38-year career by an absolute mile," Cardiff manager Neil Warnock told Sky Sports.
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"I've got a great bunch of lads. Nobody gave us a chance. I'm so proud of them. In the end we did enough.
"I've had some great promotions and squads but because of the circumstances when I came here, second bottom, it's the proudest achievement of my life," added Warnock who became the first manager in English senior football to win eight promotions.
Birmingham's win helped them avoid relegation for the second successive campaign but there was misery for Burton Albion and Barnsley, who dropped into League One after losing 2-1 to Preston North End and 4-1 to Derby County respectively.
Barnsley sacked manager Jose Morais shortly after their relegation.
Bolton Wanderers narrowly avoided the drop after staging a comeback in the closing minutes to beat Nottingham Forest 3-2.
"Strange things happen on the last day and we knew we had to keep going right until the end," Bolton manager Phil Parkinson told the BBC. "It's funny what can happen when you need to get a goal in those situations.
"... when we got the third goal, you could tell from the crowd's reaction what it meant and that we'd done it."
Champions Wolves fell to a shock 3-0 defeat at basement side Sunderland, whose relegation to the third tier was confirmed last month.
Fulham will play sixth-placed Derby in the first leg of their playoff semi-final on May 11 while fourth-placed Aston Villa face off against Middlesbrough a day later.
(Reporting by Aditi Prakash in Bengaluru; Editing by Toby Davis)
