Newcastle forward Anthony sealed a 1-0 win against Chelsea on Saturday that dealt a major blow to the Blues' bid to qualify for the Champions League.
Gordon netted in the first half at Stamford Bridge to leave Chelsea in fifth place in the Premier League.
After crashing to a 5-2 defeat at Paris Saint-Germain in the Champions League last-16 first leg in midweek, Chelsea suffered an unwanted hangover with a disjointed display in west London.
An evening that started with Chelsea's players bizarrely surrounding referee Paul Tierney during their pre-match huddle ended with the Blues' Champions League hopes in disarray.
Liam Rosenior's side trail third-placed Manchester United and fourth-placed Aston Villa by three points and have played a game more than both their top-four rivals.
United and Villa are in action on Sunday when they meet at Old Trafford, while sixth-placed Liverpool – behind Chelsea on goal difference – will go above the Blues if they avoid defeat against Tottenham on Sunday.
Newcastle were also in Champions League action in midweek, earning a creditable 1-1 draw against Barcelona at St James' Park.
And Eddie Howe's side were more vibrant than Chelsea in the early stages.
Tino Livramento's 18th-minute pass split their defence, allowing Joe Willock to burst unimpeded through the middle unchecked.
Willock provided the killer pass for Gordon and the England forward applied the finishing touch into the empty net.
CHELSEA FANS FRUSTRATED
Rumbles of discontent from Chelsea supporters were soon audible as every blocked shot or misplayed pass raised the anxiety levels.
There was little to reassure the frustrated fans in the first half as Chelsea laboured to make the most of their possession.
Willock's drive was tipped over by Robert Sanchez at his near post, while Jacob Ramsey's shot deflected off Trevoh Chalobah and required a smart save from the Blues keeper.
Sanchez, back in for the injured Filip Jorgensen, nearly produced the latest in a long line of blunders this season, but Wesley Fofana saved the keeper after his wayward pass.
Chelsea striker Liam Delap fired woefully over the bar from six yards, then Chalobah headed wide under pressure from Ramsdale.
Reece James came within inches with a late free-kick and Joao Pedro's header landed on the roof of the goal, but Newcastle held firm.