With Chelsea beating Sporting Lisbon 3-1 at Stamford Bridge, the German outfit just needed a victory in Slovenia to progress as runners-up in Group G.
After stuttering through the first half, Schalke upped the tempo after the break and should have edged ahead when Klaas-Jan Huntelaar hit the post from close range.
However, substitute Max Meyer held his nerve when calmly capitalising on a poor parry by Maribor goalkeeper Jasmin Handanovic to snatch a 62nd-minute lead shortly after coming on.
The hosts did their best to push forward in search of an equaliser, but Schalke held firm at the back and could have even added a second in stoppage time through late replacement Marvin Friedrich.
"We are very happy to be in the round of 16," beamed head coach Di Matteo, who was in charge of Chelsea when they lifted this trophy in 2012.
"That is also an important step in the development of the team. We really deserved this victory."
