Rusedski was always in command of the first set in which he conceded only three points on serve, two of them double- faults, and broke the Ferreira serve in the eighth game.
The World No 10 looked on course for a comfortable victory when he broke again to lead 3-2 in the second set. Suddenly, though, Ferreira produced some sparkling returns to break straight back.
There were no further break points in the match, but Rusedski played a superb tie-break, winning the first four points and claiming it decisively, 7-2.
Rusedski, seeded fourth, declared himself "pleased with the way I served and very satisfied with my overall performance."
He praised his new coach, Tony Pickard, for his tactical guidance. "He's watching all my matches on TV and so far his advice has been spot on. "I think it's the start of a great relationship."
Like Henman, Rusedski will face a Swede in today's quarter-final. Rusedski's opponent is the sixth seed, Thomas Enqvist, while Henman takes on the French Open semi-finalist, Magnus Norman.
Henman took advantage of poor serving from his opponent, Karol Kucera, to secure a comfortable 6-4, 6-1 win. Henman won in 66 minutes against the Slovakian, who had knocked out the third seed, Goran Ivanisevic of Croatia, in the first round.
Henman said: "I served very well, which helped when he had a couple of break points. But in the second set he started to serve double-faults, which gave me opportunities, and the more he became under pressure the more he double-faulted."Reuse content