Newcastle captain Jamaal Lascelles put his side ahead again with a header on the hour mark, and a minute later Joelinton robbed fellow Brazilian Thiago Silva on the edge of the penalty area and slotted the ball home to make it 3-1.
Any chance Chelsea had of staging a comeback vanished when Reece James collected his second yellow card in the 73rd minute, and Gordon netted a fourth goal 10 minutes later as Newcastle rose to sixth in the table on 23 points, while Chelsea are 10th on 16 points.