The Welsh club needed all three points at St James' Park to realistically have any chance of preventing an immediate return to the Championship.
But Ole Gunnar Solskjaer's men rarely looked like claiming victory, surrendering in meek fashion, with Sunderland's 1-0 success at Manchester United confirming their demotion.
A first-half header from Shola Ameobi and late goals from Loic Remy and Steven Taylor secured Newcastle's win against a backdrop of fan protests over Mike Ashley's ownership and Alan Pardew's reign as manager despite the team's dismal form in 2014.
Two separate walkouts in the 60th and 69th minutes had been planned by Newcastle fans, and large sections of the home support vacated the stadium with much of the second half still to play.
But the main storyline occurred on the pitch as Cardiff fell short in their efforts to keep prospects of safety alive.
Cardiff - who were without Gary Medel, Mats Moller Daehli and Kevin Theophile-Catherine due to illness - almost made an ideal start inside the first five minutes, Fraizer Campbell volleying narrowly wide from the edge of the area after Tim Krul punched a cross straight into his path.
Both sides struggled to create chances in the early going, but defender Mathieu Debuchy twice came close to giving Newcastle the lead.
However, the hosts did go ahead after 17 minutes, Ameobi meeting Moussa Sissoko's right-wing cross at the far post with a fine diving header that flew past the helpless David Marshall.
Sissoko was heavily involved again as Newcastle narrowly missed out on doubling their advantage just two minutes later, with the midfielder's low deflected effort hitting the post.
Cardiff's main threat came through Wilfried Zaha, who would have levelled matters if not for a great reaction save from Krul, the Dutchman sticking out a leg to preserve Newcastle's lead after the on-loan forward had cleverly worked his way into the area.
Each team made a change during the half-time interval, former Newcastle striker Craig Bellamy replacing Kim Bo-kyung for Cardiff, while Massadio Haidara took the place of Paul Dummett at left-back for the hosts.
But Bellamy's introduction failed to turn the game in the visitors' favour, and Cardiff were fortunate not to fall further behind as Mike Williamson saw an effort deflect just wide of the post.
A lack of excitement on the pitch saw attentions turn to protests off the field for much of the second period, but Cardiff found life in latter stages as they pressed for an equaliser.
First a point-blank save from Krul denied substitute Kenywne Jones a leveller, and Newcastle's lead was kept intact in spectacular fashion moments later as captain Fabricio Coloccini brilliantly cleared Aron Gunnarsson's effort off the line.
And Cardiff's fate was sealed three minutes from time, Remy coolly finishing off a Newcastle counter after collecting Sissoko's deflected pass.
Pardew's men then piled further misery on the visitors in injury time when substitute Taylor bundled the ball in from Remy's header following good work down the right from Dan Gosling.
