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.
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.
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.
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.
