Daniil and Marton played a tight match in Monte Carlo previous year and that certainly wasn't the case today, with the Russian saving two out of three break points and pushing the rival to the limits on the second serve (Fucsovics was three from 22) to create nine break chances and convert four. Medvedev is higher ranked and in better form.
Berdych was 3-5, 15-40 down on his own serve in the deciding set and staring elimination in the face but recovered to hold before breaking Krajinovic in each of his next two service games to advance to the semis. "I'm glad that things didn't get complicated and I made it to the final", said Medvedev.
Medvedev came out of the blocks fast and Klizan could not cope with the big-hitting Russian, who fired nine aces during his comfortable 6-4, 6-1 win without offering up a single break point.
Monfils will now take on Radu Albot in the semi-final, after the Romanian got the better of Marcos Baghdatis in another quarter-final match.
Frenchman Gael Monfils registered a huge shock at the Sofia Open when he usurped the second seeded Stefanos Tsitsipas to book his place in the semi-finals.
The two players were meeting for the first time on the ATP Tour and made it a contest to remember.
In the second straight all-French final in Montpellier, Tsonga becomes the seventh French victor in the tournament's nine-year history.
Berdych, who is unseeded at the tournament he won in 2012, then turned the match around.
Injury-plagued Jo-Wilfried Tsonga claimed the 17th title of his career on Sunday when he defeated French compatriot Pierre-Hugues Herbert 6-4, 6-2 to claim the Montpellier title.