Both sides came into the game unbeaten from their first two matches of the season but it was Wolfsburg, missing Manchester City-bound Kevin de Bruyne and reported Inter Milan target Ivan Perisic, who took control of proceedings early on.
A patient passing move saw the ball worked out wide to Christian Trasch, whose superb cross found Dost unmarked six yards out, and the Dutch international volleyed home his second goal of the season to give Dieter Hecking's side a deserved lead.
Wolfsburg continued to dominate after the breakthrough with Vieirinha firing over from 25 yards, but Schalke could have equalised against the run of play when Leroy Sane's hesitation allowed Naldo to get in a crucial recovery challenge.
That chance signalled something of an awakening for the visitors, who visibly grew in confidence and carved out another opportunity when Sane could not convert from Sascha Riether's cross.
Andre Breitenreiter's side should have been level on the half-hour mark after Wolfsburg lost possession in a dangerous area, but Klaas-Jan Huntelaar was unable to keep his effort down after being picked out by Maxim Choupo-Moting.
Riether almost gifted the home side a second with a weak pass back to Fahrmann, but the Schalke goalkeeper was able to recover to prevent Max Kruse from taking advantage of the error before the whistle.
Live commentary of the second half can be found here.