Marco Hoger put the hosts in front before Boateng, who arrived from AC Milan on Friday, went close to marking his debut with a goal.
Instead, it was Jefferson Farfan who sealed a 2-0 victory from the penalty spot in the 83rd minute as Leverkusen dropped points for the first time this term.
Boateng went straight into the Schalke starting XI, with Dennis Aogo also making his debut at the back.
The new-look Schalke took the lead after half an hour when Hoger got the slightest of touches with his head to Farfan's free-kick, helping the ball on its way past Bernd Leno.
Leverkusen responded with Heung-Min Son shooting just wide from outside the penalty area, but Schalke held their lead going into the break.
Timo Hildebrand mad a fine save to push another Son effort behind for a corner after 62 minutes before Boateng went agonisingly close at the other end.
Leno made a fine one-handed save to keep out the Ghana international's header from point-blank range as he met Adam Szalai's cross.
Leverkusen tried to hit back, committing more and more players forwards, but failed to find a route to the well-marked Stefan Kiessling.
On the break, Farfan burst into the area and was brought down by Emir Spahic inside the penalty area, and the Peruvian stepped up to send the ball into the top-left corner from the spot
Late on, Christian Clemens wasted a gilt-edged chance when he shot wide of an open goal, but the damage had already been done as Schalke picked up their first win of the season with Leverkusen losing for the first time.