Goals either side of half time from Zenit St Petersburg winger Robert Mak and an Adam Nemec header were the Tartan Army's undoing as they slumped to a reverse that piles the pressure on manager Gordon Strachan.
There was a measure of controversy about Mak's opener, which came in the 18th minute moments after the Scots had appealed vociferously for a foul on Steven Fletcher.
Unbeaten in Group F ahead of kickoff, Strachan's side saw plenty of the ball but showed no creativity in the final third, and Mak further punished them in the 56th minute when he sped away from Russell Martin and drilled the ball beyond Marshall.
Slovakia's third was the result of a textbook corner, which Mak swung in from the left as Nemec outjumped Grant Hanley to nod home unchallenged and put the hosts out of sight.
The result sees Slovakia pick up their first win of the qualifying campaign to move within a point of fourth-placed Scotland in Group F after three matches.