Days after collapsing on the red dirt of Paris following his second-round victory in sweltering conditions, Mensik shone on a cool evening following a spell of rain to book a last-four clash with title favourite Alexander Zverev.
After four straight holds of serve to kick off the contest under the Court Philippe Chatrier roof, the momentum swung when Mensik edged ahead with a break, and the 20-year-old Czech stayed firm from there to win the opening set.
The ice-cool Mensik tightened his grip on the contest when the second set unfolded in a similar fashion, as the 19-year-old Fonseca's serve let him down in a crucial moment and he then struggled to find a way past the wall in front of him.
The youngest Roland Garros men's quarter-final since a 20-year-old Rafa Nadal defeated a teenage Novak Djokovic in 2006 looked in danger of becoming a rout as Mensik bagged the set when his opponent pushed a shot wide.
With his adoring Brazilian fans stunned and the frustration rising, Fonseca came out firing in the third set, but was broken when serving for it at 5-4. Mensik drew level before wasting six match points and eventually prevailing via a tiebreak.