Laurent Depoitre opened the scoring for the Terriers early in the second half and although Marcos Alonso equalised in fortuitous circumstances, David Wagner's team held out to ensure that their survival efforts did not go to the final day of the campaign.
As for Chelsea, they can only secure a top-four place in the standings with victory at Newcastle United on Sunday, coupled with a Brighton & Hove win against Liverpool at Anfield.
Chelsea required just six minutes to create their first opportunity of the game with Cesc Fabregas's cross-field ball being controlled by Alonso before a well-struck volley was turned away by goalkeeper Jonas Lossl.
Willian then fired wide from 30 yards out but the Blues should have opened the scoring through Antonio Rudiger, who somehow diverted the ball wide from close range at the back post after a header from Cesar Azpilicueta.
Huddersfield began to find their feet at Stamford Bridge to frustrate the Blues - much like they did against Manchester City at the weekend - but Alvaro Morata almost found the bottom corner with a volley after meeting a pass from Fabregas.
Morata had a better opportunity just before the break. The Spaniard was played through on goal but after deciding to round Lossl, the frontman was only able to shoot from an acute angle and the ball went straight across the face of goal.
Soon after the restart, Rudiger headed over from a Willian free kick as Chelsea threatened to regain control but moments later, Huddersfield went in front with their first shot on goal.
Depoitre ran onto a long ball and got there ahead of goalkeeper Willy Caballero, who was left injured after a collison with the forward, but the Belgian's challenge was fair and after Rudiger slipped in front of him, the ball was tapped into the net from 12 yards.
A cross from the right was cleared into the face of the Spaniard and despite not knowing anything about it, the ball found the bottom corner of Lossl's net with the goalkeeper left with no chance to react.
The Chelsea pressure which followed was relentless but the home side were struggling to create clear-cut openings as Huddersfield packed each of their 10 outfield players behind the ball.
With seven minutes left, that chance arrived for Andreas Christensen who kept his composure amidst a goalmouth scramble, but the Dane's header was brilliantly tipped onto the post by Lossl.
As full time edged ever closer, Morata's fierce effort was palmed away by Lossl but after the fourth official indicated that six minutes would be added on, Chelsea still believed that they could force a late winner.
However, a final opportunity did not arrive and Huddersfield were left to celebrate in front of their travelling supporters, with Chelsea left to contemplate a probable year in the Europa League.
CHELSEA (3-4-3): Caballero; Azpilicueta, Christensen, Rudiger; Zappacosta (Giroud 54'), Kante, Fabregas, Alonso; Willian, Morata, Pedro (Hazard 59')
HUDDERSFIELD TOWN (5-4-1): Lossl; Smith (Malone 85'), Jorgensen, Schindler, Kongolo, Lowe (Hadergjonaj 62'); Hogg, Billing, Mooy, Van La Parra (Pritchard 53'); Depoitre