The 29-year-old, who has lost three major finals, including one at Roland Garros two years ago, has looked sharp in Paris and faces the winner of the all-Italian clash between 10th seed Flavio Cobolli and Matteo Arnaldi.
A tight opening set on a sun-kissed Court Philippe Chatrier tilted Zverev's way when he struck a backhand crosscourt winner in the 11th game to bring up a break point, and he nudged ahead with a delicate shot that Mensik sent into the net.
"I knew that it would be my toughest challenge. I managed it and I won, so I'm happy," said Zverev, who became only the fifth active player to reach multiple Roland Garros title clashes.
"It's amazing the way he (Mensik) played these last two weeks, he beat so many unbelievable players. He started playing amazing in the third set, stepping up his level, but this is a Grand Slam with best-of-five-set matches.
"Things happen and your opponents will play better. You have to deal with it. I hope to play another great match on Sunday."
The world number three sent down a powerful ace to pocket the first set and asserted himself with an early break at the start of the second set, as the 20-year-old Mensik's level briefly dipped in his maiden Grand Slam semi-final.
Mensik sat with a towel over his head during a changeover, and his troubles deepened after the restart, when Zverev took his game up a few notches and sealed a double break, before comfortably doubling his lead in the match.
After a long medical timeout for a neck issue, Czech Mensik mixed his booming serve with deft drop shots to break for a 4-2 lead en route to winning the third set, but Zverev powered through the next with no drama to prevail.