The 21-year-old Austrian held off the challenge of German Felix Loch to fly across the line in 35.835 and take a momentous gold in his fledgling career.
Mueller was the quickest out the blocks in the competition and it worked to his advantage as he sealed the win by just 0.024s to edge three-time Olympic champion Loch into silver.
Meanwhile, 2015 World Championship gold medallist Semen Pavlichenko sealed a first sprint medal of his career by finishing in 35.889 to complete the podium.
2018 World Champion Wolfgang Kindl could only muster an eighth-place finish on the German artificial track.
Round 5, Oslo