The German, a semi-finalist in 2014 and 2017, saved three set points when Munar served for the first set at 5-4. Kohlschreiber broke early in the second set and will next play sixth-seeded Serbian Filip Krajinovic or fellow German wild card Daniel Altmaier.
Earlier in the day, Brazilian qualifier Thiago Seyboth Wild recorded his first tour-level victory of the season, 1-6, 6-1, 6-2, over Spanish wild card Nicola Kuhn in just under two hours. The Brazilian qualifier awaits the winner of seventh-seeded German Jan-Lennard Struff and Laslo Djere of Serbia.
Argentine lucky loser Sebastian Baez swept past Corentin Moutet of France 6-1, 6-2 in 63 minutes and will next challenge third-seeded Georgian Nikoloz Basilashvili, the 2018 and 2019 titlist. Baez is currently in eighth position in the ATP Race To Milan for a spot at the Next Gen ATP Finals.