The Reds have only won one Premier League game in their last five.
The lead lasted just 13 minutes though as Marcos Alonso levelled when Cesar Azpilicueta's cross was drilled against the full-back and rebounded into the net.
Chelsea kept up the pressure as they pushed for a victor and Huddersfield keeper Jonas Lossl turned a header by Andreas Christensen on to the post.
Huddersfield have held the champions from the past two seasons in the last four days to ensure they can not now finish in the Premier League's bottom three.
Asked how he planned to celebrate with the squad, Wagner replied: "The guys just said we cancelled their flight".
"This is an unbelievable achievement". "For sure, we had our luck, for sure, Chelsea were the better team". Today was a stolen point but, to be perfectly honest, I don't care.
Under the circumstances we started the season, for a football club of our size, we are anything but a Premier League club, but we were in this competition and we said, 'Come on'. "We love games like this, we knew what we needed, a point".
This was a must-win game for both teams as a draw for Huddersfield will see them avoid relegation, whereas for Chelsea a draw or a loss could potentially mean they will not finish in the top 4.
"The only hope and intention was to keep our hopes alive and win the game".
Chelsea manager Antonio Conte has intimated that his future will become clearer at the end of the season when the Blues have finished all of their upcoming fixtures.
"We had the chances to score, but we didn't take them". For only the third time ever in the EPL, all three promoted sides achieved safety in their first attempt.
"[It] will be a hard game but we have one week - that feels like a year and we will use that".
Depoitre fired Huddersfield ahead against the run of play with 50 minutes on the clock. "We were so unlucky, we dominated the game and conceded a silly goal and then we couldn't score [a second goal]".
The point at Stamford Bridge follows a goalless draw against Manchester City at the Etihad Stadium last time out.
"To be totally honest my English isn't good enough to describe what the players have done over the whole season", Wagner told Sky Sports.
Conte had a wonderful first season in charge, winning the 2016/17 Premier League title easily, but things have not gone according to plan this time around. They tried to get three points.
"We knew it was going to be a tough game, they're very good on the ball so we had to get closer and make it hard, so we did it quite well", Mooy said.
"We must give compliments to Huddersfield for this result...congratulations to the club".