The home side otherwise played an excellent first half, where the game basically could have been decided.
Only three minutes had been played when Patrick Mortensen put AGF ahead.
Gift Links, who before kickoff added three years to his contract so that it now runs until 2029, broke free on the left wing and produced a perfect delivery for Mortensen, who was left with an easy tap-in.
Mortensen had several chances to score further in the first half. Especially shortly before half-time, when Kristian Arnstad won a penalty for the home side.
Randers-keeper Jannich Storch dived well to save Mortensen's first attempt, but Mortensen was surprisingly handed another attempt when the referee adjudged Storch to have left the goal line before the kick. Mortensen, who has only wasted two penalties in his career in the Danish Superliga, then went for more power, but Storch also managed to save that attempt.
Jesper Hansen, who replaced Leopold Wahlstedt in goal in the wake of last week's disappointing draw at Sonderjyske, was not tested in the first half but that changed significantly from the start of the second half. After just seven minutes, Randers had turned 0-1 into 2-1.
First, Mohamed Toure served the ball on a platter for Norman Campbell, who made no mistake from close range, and two minutes later, Campbell then provided the layup for Elies Mahmoud to score via the post.
The goal completely changed the momentum of the match, as AGF found it difficult to regain control.
Randers was closer to making it 3-1 than AGF was to equalise, as Mathias Greve came very close in two situations.
AGF tried to add pressure in the final phase, but Randers held on to pick up three prestigious points against their bitter rivals.