Leverkusen announced before Saturday's kickoff that Jonas Hofmann will be out for the rest of the year with a right thigh injury from training, adding to an injury list including Victor Boniface, Amine Adli and Nordi Mukiele.
Heidenheim then stunned the defending champions when Marvin Pieringer won the ball from Piero Hincapie and set up Niklas Dorsch to open the scoring in the 10th minute.
Mathias Honsak surged past three Leverkusen defenders and shot inside the far post to make it 2-0 11 minutes later.
Exequiel Palacios pulled one back in the 30th, two minutes before Schick equalised with a deft chip over the Heidenheim goalkeeper.
Florian Wirtz crossed for Schick's second goal in the 52nd and substitute Arthur crossed for his hat-trick in the 71st.
Granit Xhaka completed the scoring before celebrating by sucking his thumb and making a baby gesture.
Leverkusen's injury concerns increased with Jeremie Frimpong limping off before the break and Martin Terrier going off late with an apparent hand injury.
Hosts Borussia Dortmund beat Freiburg 4-0, easing the pressure on Nuri Sahin after four league defeats already this season. The visitors finished the game with nine players.
Dortmund were without Serhou Guirassy because of illness.
Before the match, Freiburg fans had protested against the home team's sponsor, the arms manufacturer Rheinmetall, with banners referring to the company with an expletive, and another saying, "No war on people, war on the federations!"
The sponsorship deal is set to be a major topic at Dortmund's AGM on Sunday.
Mario Götze scored on his 100th Eintracht Frankfurt appearance in a 1-0 win over visiting Werder Bremen.
The German midfielder rifled the ball in before the break after a good layoff from Hugo Ekitiké.
Frankfurt star Omar Marmoush worked hard but was unable to add to his 11 league goals so far this season.
The win lifted Frankfurt to second, six points behind Bayern Munich.
Jacob Bruun Larsen scored late for Hoffenheim to beat Leipzig 4-3 in coach Christian Ilzer's debut. Ilzer's team came from behind three times to prevail.
It's Leipzig's fourth straight game without a win.
Stuttgart enjoyed a 2-0 win over Bochum, and Wolfsburg defeated Union Berlin 1-0.
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