The Welsh club's fate was sealed after Newcastle's bitter rivals Sunderland triumphed 1-0 at Manchester United.
However, a Tim Krul error almost handed Cardiff the lead. The Dutch goalkeeper saw his weak punch fall at the feet of Frazier Campbell, but the forward's effort from 18 yards drifted harmlessly wide of the post.
David Marshall then denied Mathieu Debuchy twice in two minutes. First, the goalkeeper tipped the Frenchman's strong effort wide before getting his fingertips to his header from the resulting corner to divert it onto the bar.
Marshall was helpless to prevent the opener though, as an unmarked Shola Ameobi nodded home at the far post in the 18th minute and registered just his second league goal of the campaign.
© Getty Images
Just four minutes later, Moussa Sissoko crashed a long-range shot against the foot of the post as Cardiff struggled with Newcastle's pace and power in attack.
Wilfried Zaha took matters into his own hands and tested Krul twice in a matter of minutes, but Newcastle reminded the visitors of their attacking prowess when Sissoko hit the post once again with a deflected cross.
Craig Bellamy replaced Kim Bo-Kyung at the break as Ole Gunnar Solskjaer looked for a way back into the game, but Newcastle almost went 2-0 ahead in the 57th minute when Mike Williamson's speculative effort took a wicked deflection and spun inches wide of Marshall's post.
As was widely reported in the lead-up to the game, a large proportion of the home fans left the stadium in the 69th minute in protest against the club's owners. On the pitch, there was little in the way of second-half action until the 75th minute.
First, Kenwyne Jones headed at Krul with his first touch since coming on as a substitute. Then, Aron Gunnarsson pounced when Krul spilled the ball at his feet, only for Fabricio Coloccini to throw his body in the way of the Icelandic's goalbound effort.
With Cardiff pushing for a goal of their own, Remy found space on the left wing before cutting inside, but his curling shot was deflected wide.
With just three minutes remaining, Cardiff's fate was sealed when Remy fired home a rebound after Sissoko's initial shot was saved and substitute Steven Taylor put the icing on the cake in the 90th minute with a third goal.