The former Barcelona forward netted for the first time since joining Mark Hughes's side this summer but the Bundesliga side's class saw them through to victory in Austria
A week after signing for the Premier League club from Barcelona, Bojan showed exactly why the Potters brought him to the Britannia Stadium with a stunning goal just after half-time.
However, the 23-year-old's effort was in vain, as the Bundesliga club rallied to win Tuesday's pre-season friendly.
After an entertaining but goalless opening half, Bojan broke the deadlock 10 minutes after the restart by firing home from the edge of the box after beating two defenders.
Hughes's side were only ahead for three minutes, though, as Schalke defender Joel Matip rose unmarked at the back post to level with a bullet header.
And victory was assured for the Germans when Swiss winger Tranquillo Barnetta found himself unmarked in the centre of the penalty area in the 85th minute before producing a composed finish.
Schalke began the game strongly, with Stoke goalkeeper Asmir Begovic - making his first appearance since returning from Bosnia-Herzegovina's World Cup campaign - forced into several fine saves.
But the Potters had the best opportunity of the first half - Marko Arnautovic missing a 40th-minute penalty after he was brought down in the area.
The Premier League club still went ahead courtesy of Bojan but Matip and Barnetta were on hand to turn the game on its head.