Ajax won their first Champions League match of the season on Tuesday after coming out on top 2-1 in a tight Group D contest at Midtjylland.
Antony's first-minute strike and a free-kick from captain Dusan Tadic, who had been expected to miss the match in Denmark following a positive coronavirus test alongside three other key players, were just about enough to see Erik ten Hag's side through.
The Dutch giants move up to second in their group, level on four points with third-placed Atalanta but five behind leaders Liverpool after they strolled to a 5-0 win in Bergamo.
Dutch media reported on Monday that Tadic, goalkeeper Andre Onana and midfielders Davy Klaassen and Ryan Gravenberch would all be absent but the quartet made the trip to Denmark.
Three of the four started in Herning and Tadic was key to Ajax's win, setting up Antony's opener just seconds after kick-off before thrashing home a 13th-minute free-kick from close range after Midtjylland goalkeeper Mikkel Andersen collected a back pass inside his own area.
Anders Dreyer pulled one back in the 18th minute when he cut inside from the right and beat Onana at his near post with a powerful shot.
Antony thought he had restored the away side's two-goal lead when he slipped a lovely finish past Andersen from a tight angle but the goal was chalked off for offside after a VAR check.
That setback didn't stop Ajax from earning a win that gives them an advantage in the group going into the fourth round of matches later this month, when they host bottom side Midtjylland in Amsterdam while Atalanta have to travel to Anfield to face Liverpool again.