The French Ligue 1 side, who had lost their first three games in a competition that looked too big for them, still lie bottom of Group G but they now trail second-placed AC Milan, whom they host in three weeks, by only two points.
Steeven Langil's strike six minutes from time settled it after Toby Alderweireld had levelled Frederic Sammaritano's early goal for the French.
Substitute Langil caught the Ajax defence napping when he collected a quickly played Kamel Chafni free kick before coolly slotting home at the packed Abbe Deschamps stadium.
The result leaves Auxerre on three points, one behind the Dutch and seven adrift of runaway group leaders Real Madrid who have already qualified courtesy of their 2-2 draw with Milan.
"It is good for our pride," Auxerre coach Jean Fernandez told French TV channel Canal Plus.
"Now we will play Milan with more confidence as we're also on a good run in the league.
"We had played well in our first three games in the competition but we were not lucky enough. Tonight, we were."
Ajax made a good start when Urby Emanuelson's shot whizzed just over the bar in the seventh minute but it was Auxerre who scored first through Sammaritano, who joined the club late in the August transfer window from Ligue 2 side Vannes.
Julien Quercia chested the ball into his path and Sammaritano volleyed home from just outside the box in the ninth minute.
Ajax piled on the pressure and Luis Suarez moved from the left to the right flank, causing huge trouble for the Auxerre defence.
He came very close six minutes before the interval but after dribbling past a couple of Auxerre players, the Uruguay striker's angled shot shaved Olivier Sorin's right post as Auxerre hung on to their slim advantage.
Ajax, however, hit back with 11 minutes left when Alderweireld headed home from a corner but Langil, who came on as a 63rd minute substitute, took advantage of a lapse in concentration to give Auxerre all three points.
"It was well deserved, especially after we played actually pretty well in our first three games but did not get a point," captain Benoit Pedretti told Canal Plus.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.