Bohar, who scored two goals in the qualifying rounds to help Maribor return to the group stage after a 15-year absence, silenced the Veltins-Arena crowd following a superb passing move before half-time.
Klass-Jan Huntelaar then capitalised on a defensive error to equalise, with what was his 24th goal in 31 European appearances for Schalke.
However, despite Jens Keller's side's late pressure, the Slovenian champions held on to make it two points from two outings in Group G.
Schalke recovered from their worst start to a season since 1967-68 by recording back-to-back wins over Werder Bremen and arch-rivals Borussia Dortmund, but this setback leaves them having won just one of their last eight Champions League matches.
Schalke talisman Julian Draxler returned from suspension in place of the injured Sidney Sam, while Keller chose to start Tranquillo Barnetta ahead of Max Meyer.
Draxler was involved in creating the game's first chance for Huntelaar, whose firm strike was saved by Jasmin Handanovic, before Maribor almost punished their hosts with a goal reminiscent of David Beckham's celebrated strike for Manchester United against Wimbledon all those years ago.
Noticing Ralf Fahrmann off his line, Dare Vrsic unleashed a shot from inside his own half, which looped over the Schalke goalkeeper but went narrowly over the crossbar.
Schalke had a great opportunity to break the deadlock midway through the half.
Christian Fuchs looked up and produced a fine cross from the left for Kevin-Prince Boateng, who - despite being unmarked at the back post - headed wide.
Fahrmann did well to gather a fierce low strike from Marcos Tavares, but he was powerless to stop Maribor going ahead eight minutes before the break.
A slick one-touch passing move freed Mitja Viler down the left and, rather than squaring it across the box for Tavares, he cut a deceptive pass back into the path of Bohar, who fired the ball home from 10 yards.
Schalke levelled 11 minutes after the restart with a gift of a goal.
Viler needlessly passed the ball to Huntelaar on the edge of the box. The 31-year-old cut inside and although Handanovic got a hand to his strike, the goalkeeper was unable to prevent it creeping into the bottom corner.
Handanovic then made a one-handed save to deny Draxler on the hour, before Boateng volleyed wide.
Schalke continued to pursue a winner, but Marko Suler made one vital interception to deny substitute Meyer a chance and Barnetta had a volley blocked before the final whistle.
