By Julien Pretot
World number 23 Verdasco needed a set to adjust to Cilic's big serve before easing past his Croatian opponent in front of a sparse audience at Bercy.
Czech Berdych, the fifth seed, will make sure he takes part in the season-ending ATP World Tour finals in London if he reaches the quarter-finals in Paris.
Seven players taking part in the Paris tournament are vying to clinch one of the three remaining spots for the November 20-27 finals at the O2 Arena.
Cilic converted his only break point to wrap up the first set but Verdasco broke in the second game of the second set, then held serve to level the match.
After that he never looked back.
Tsonga will also definitely qualify for London by reaching the quarter-finals, as will American Mardy Fish.
(Reporting by Julien Pretot; Editing by Martyn Herman)