Murray made the last eight for the fifth straight year by beating the 16th-seeded Marin Cilic 7-5, 6-2, 6-3, while Mayer ousted Richard Gasquet of France 6-3, 6-1, 3-6, 6-2. American qualifier Brian Baker's remarkable run ended with a 6-1, 7-6 (4), 6-3 loss to 27th-seeded Philipp Kohlschreiber of Germany.
Rain had prevented five of the men's fourth-round matches from being completed on Monday. The weather continued to cause headaches as the start of play on outside courts was delayed for about 30 minutes because of light showers. When matches started, they were quickly halted again for another rain delay of about an hour.
''We stopped, obviously, a lot,'' Murray said. ''You're always a little bit edgy when you come out after a rain delay when you have the momentum with you. You stop, and then you come back out, and it feels a bit like you start from scratch again. I needed to serve well today and I got a lot of free points that helped me out.''
Play on Centre Court didn't even have time to start at all before the rain came. Organizers had closed the roof because of earlier showers in the morning but then decided to open it during a dry spell just before Ferrer's match against del Potro. When the showers resumed, they promptly had to close it again and keep the players waiting.
When the match began, Ferrer needed less than two hours to beat del Potro 6-3, 6-2, 6-3. Another rain delay then forced the suspension of Jo-Wilfried Tsonga's match against Mardy Fish, with the fifth-seeded Frenchman leading 4-6, 7-6 (4), 6-4, 4-2. Tsonga went on to win the match 6-4 in the fourth set.
Murray's match was halted on Monday with the Briton leading 3-1, 40-0 in the second set. He had time to play one point on Court 1 - clinching that game - before rain started falling again. One game later, the match was suspended once more. After the second resumption, there was another slight break early in the third set as the players remained in their chairs for about five minutes under umbrellas as officials waited for a light shower to subside.
The Briton's victory never looked in doubt, though, and he served out the match to love when the Croat netted a backhand. Murray will next play Ferrer as he tries to become the first British man to win Wimbledon since 1936 - a task that looks easier after Rafael Nadal was knocked out in the second round last week.
The 126th-ranked Baker was trying to become the third American qualifier to reach the quarterfinals at the All England Club. He was playing in Wimbledon's main draw for the first time after being off the tour for more than five years because of a series of operations, one on his right elbow. He was ranked 458th at the start of 2012 but now will rise inside the top 100.
On Monday, top-ranked Novak Djokovic, Roger Federer and Mikhail Youzhny were the only men to complete their round of 16 matches.