After Tino Livramento released Joe Willock with a defence-splitting pass, Gordon's burst forward was rewarded with a neat lay-off from Willock, giving the England international a simple finish to put the Magpies one up after 18 minutes.
And that's the way it stayed at Stamford Bridge, as Eddie Howe's determined charges impressively kept the Blues at arm's length to take all three points and make it back-to-back Premier League victories.
The game's decisive moment, though, came somewhat against the run of play. After a bizarre pre-match scene as the hosts conducted their team huddle around referee Paul Tierney, Wesley Fofana headed a Reece James corner over in the first real opening of the evening.
Alejandro Garnacho robbed Nick Woltemade and saw his weak effort collected by Aaron Ramsdale, before Cole Palmer picked up Malo Gusto's cutback and sliced just wide of the target.
Captain Enzo Fernández then saw his drive strike Palmer in the face quarter of an hour in as Liam Rosenior's men continued to push, but Gordon's opener - his 16th of the season in all competitions - stymied their strong start. It owed a lot to Livramento's incisive through ball for Willock, who teed up a tap-in for the frontman.
Newcastle began to find some more gaps in the Chelsea backline after Gordon's goal, with Willock forcing Robert Sánchez to awkwardly tip over his attempt from the tightest of angles and Malick Thiaw unlucky not to be awarded a penalty after James hauled him over from the resulting corner.
And Ramsdale made a fairly routine stop from Palmer before the break as the Blues looked to regain some of their earlier rhythm, but to no avail. A wayward James free kick from 25 yards was all they could muster before the end of the half, with Jacob Ramsey going close to making it 2-0 in stoppage time when his deflected drive was parried by Sánchez.
Substitute Liam Delap forced a smart save from Ramsdale after the restart but momentum continued to evade Rosenior's men. A lot of that was because of United's discipline and resoluteness; Garnacho saw a shot charged down on the edge of the box, before Marc Cucurella fell over while attempting to turn the rebound back across goal.
Just after the hour mark, Chelsea felt aggrieved not to have been given a penalty by Tierney after Palmer tumbled under the challenge of the industrious Woltemade, but they still couldn't work out a way of breaking down the Newcastle rearguard.
Gordon offered a reminder of the Magpies' threat, testing Sánchez with just under a quarter of the contest remaining, while Delap lashed a big chance over the bar after Cucurella had turned James' cross back into his path. James' crossing did cause a few problems, with Trevoh Chalobah heading another delivery wide.
But while they were forced to retreat in the closing stages, with James' swerving free kick striking the base of the post in added time, this was a merited win for Howe's men whose resilience came to the fore as they hauled themselves into the top half of the table.
Newcastle United: Aaron Ramsdale, Lewis Hall, Sven Botman, Anthony Gordon, Harvey Barnes, Malick Thiaw, Tino Livramento, Jacob Murphy (c) (Anthony Elanga 77), Nick Woltemade (Joelinton 67), Joe Willock (Dan Burn 77), Jacob Ramsey
Subs not used: Nick Pope, John Ruddy, Kieran Trippier, Yoane Wissa, Will Osula, Alex Murphy
