The Terriers sit on 37 points, four clear of 18th-placed Swansea City with one game left to play.
Laurent Depoitre gave the Terriers the lead in the 50th minute only to see Marcos Alonso level for the Blues in the 62nd minute.
Huddersfield goalkeeper Jonas Lossl made a brilliant fingertip save in the 83rd minute to deny Andres Christensen that all but seal his club's safety.
The Terriers' last game against Arsenal, also the final game of Gunners manager Arsene Wenger's career, will be played at home as a celebration of the remarkable achievement of the club this season.
"We've done it on our own", says Wagner
Not needing to count on other teams to help them stay up, Wagner said: "We didn't have to rely on other teams, we've done it on our own" while adding that "nobody expected it apart from us" and that "this achievement for our football club is just incredible, especially with a run-in of City, Chelsea and Arsenal.
Adding that "this is an unbelievable achievement, we have a further season in the Premier League."
The German also went on to say: "Everyone knows the circumstances that our club competes with these top clubs. For sure, we had our luck, for sure, Chelsea were the better team.
"We stole a point but we don't care".
Togetherness, belief trademark of club's survival according to German
Praising his players, Wagner said: "The dressing room has shown such togetherness all season, they always believed that in football the impossible is possible and we have done it".
He added that "we expected to work our socks off and to show the spirit, the desire, the passion and the hunger and we got our reward".
Wagner continued by saying: "This is exactly what we ask of ourselves. We know our opponents have more individual quality so you have to find a solution".
The German also felt:"We have improved over the season. We love games like this, we knew what we needed, a point.
"We were only in the bottom three once all season."