Joelinton scored just 90 seconds after Jamaal Lascelles had restored Newcastle's lead
Lascelles' free header from Gordon's cross gave the Magpies a 2-1 lead on the hour mark, before Joelinton capitalised on a Thiago Silva error to double the hosts' advantage just 90 seconds later.
And Gordon netted his fifth of the season with seven minutes remaining to put the seal on a comprehensive victory for Newcastle, who lost at Bournemouth in their previous match.
Fit-again Alexander Isak had opened the scoring in an entertaining first half, sending a composed finish beyond Chelsea goalkeeper Robert Sanchez from 17-year-old Lewis Miley's threaded pass.
Raheem Sterling's delightful free-kick restored parity 10 minutes later, but the visitors were architects of their own downfall in the second half as Lascelles and Joelinton put the game out of Chelsea's reach.
They were reduced to 10 men when Reece James was shown a second yellow card for a foul on Gordon, who completed the scoring late on.
Newcastle's fifth straight home league win moves them to within three points of fourth-placed Tottenham, while Chelsea stay on 16 points.
-- Courtesy of BBC Sport