It was an uneventful opening to the match, but the contest came to life in the 18th minute when Hertha were reduced to 10 men after Vedad Ibisevic caught Meyer with a dangerous tackle from behind.
Schalke responded to being handed the advantage by taking control of the game for much of the first half ,and Ibisevic's moment of madness was punished further when the hosts took the lead.
Andre Breitenreiter's side struggled to create more clear chances after breaking the deadlock, and they were given a warning before the break when Genki Haraguchi's low strike was saved by Ralf Fahrmann.
Leon Goretzka was twice left frustrated as Schalke caused problems for the Hertha defence early in the second half, with the midfielder sending a header straight at Rune Jarstein, before nodding wide from a corner just a couple of minutes later.
Schalke were in complete control for much of the game, but they struggled to kill the visitors off as Jarstein produced a save to keep out a Geis free kick which looked to be heading for the top corner.
Their struggles to find a second goal ensured that Hertha retained hopes of claiming an unlikely point, and Mitchell Weiser was inches away from finding the equaliser when his powerful strike clipped the post.
It was a sign of what was to come from Hertha, as they earned a reward for their resilience when Salomon Kalou found the space to head home from Weiser's cross.
© Getty Images
After leading for so long, Schalke struggled to respond to the leveller and they almost lost the game late on when Fahrmann was forced to get a crucial hand to Fabian Lustenberger's header.
However, it was Schalke who snatched the win in stoppage time as Leroy Sane sliced open the defence to find Meyer, who kept his composure to score the winner with a fine finish.