Malisse, seeking his first title since 2007, will next face the winner of a later match between Spanish third seed Fernando Verdasco and eighth seed Marcos Baghdatis of Cyprus at the 1.4 million-dollar hardcourt tournament.
Eighth-ranked Berdych struggled throughout his first tournament since losing his first Grand Slam final to Rafael Nadal at Wimbledon. He also made a run to the French Open semi-finals but has yet to win a title this year.
Berdych sent a backhand long to hand 62nd-ranked Malisse a break in the fourth game of the third set and the Belgian broke again in the eighth as Berdych hit a backhand long to end the match after two hours and 10 minutes.
Berdych surrendered breaks in the third and fifth games of the match to trail 4-1, the last coming on a video replay challenge that ruled a forehand landed beyond the baseline.
Berdych broke back in the eighth game but hit consecutive errant forehands in the 10th to allow Malisse to hold and claim the first set.
Malisse double faulted on the only break point of the second set to give the Czech a 5-3 lead and Berdych held to force a third set.
Former world number three David Nalbandian, the 2002 Wimbledon runner-up who is playing in his first event since April due to a left hamstring injury, was set to face France's Gilles Simon in a later quarter-final.
Nalbandian helped advance Argentina into the Davis Cup semi-finals against France last month and has lost only nine games in three matches.
Simon beat US second seed Andy Roddick 6-3, 6-3 in the third round, ensuring the ninth-ranked American will tumble from the top 10 next week.
It will be the first time that no US man has been in the top 10 since the ranking system began in 1973.
Nalbandian or Simon will face either Croatian fourth seed Marin Cilic or Serbian Janko Tipsarevic on Saturday for a berth in Sunday's final. Cilic is 4-0 lifetime against Tipsarevic.