British fourth seed Murray beat Croatian 16th seed Cilic 7-5, 6-2, 6-3 as organisers scrambled to make up for lost time caused by heavy rain.
| Britain's Andy Murray plays a forehand during his Wimbledon fourth round men's singles match against Croatia's Marin Cilic on July 2. |
He will now attempt to go on to a fourth All England Club semi-final on the trot, but will first have to get past seventh-seeded Ferrer who put out former US Open champion Juan Martin del Potro 6-3, 6-2, 6-3.
Also making Wednesday's quarter-finals were Florian Mayer and Philipp Kohlschreiber.
It's the first time since Wimbledon in 1997 that two German men have made the last eight of a Grand Slam.
Mayer, the 31st seed, defeated Richard Gasquet of France, 6-3, 6-1, 3-6, 6-2 in another match which was held over from Monday.
For 27th-seeded Kohlschreiber, it was a particularly memorable day as he reached his first Grand Slam quarter-final at the 33rd attempt by clinching a 6-1, 7-6 (7/4), 6-3 win over American qualifier Brian Baker.
Murray had led Queen's Club winner Cilic, against whom he was defending a 5-1 career record, 7-5, 3-1 overnight when play was suspended due to Monday's downpours.
They played two games Tuesday before more rain sent them off Court One for an hour.
But on the resumption, the Scot was rarely troubled as Cilic struggled with his opponent and the damp, chilly conditions.
"I don't see Ferrer as a clay court specialist. He won last week on grass (in 's-Hertogenbosch), so he's won, what, eight matches in a row on the grass," said Murray.
"He's been in the semi-finals of Australia and now he's starting to play better on grass."
Only three of the scheduled last 16 men's ties had been completed on Monday with Novak Djokovic, Roger Federer and Mikhail Youzhny able to enjoy a day off before Wednesday's quarter-finals.
Federer will play Youzhny on Wednesday looking for a 14th win in 14 matches against the Russian.
Defending champion Djokovic will tackle Mayer, who has reached the quarter-finals for the second time, eight years after his first appearance, with his victory over Gasquet.
It was Mayer's first win over 2007 semi-finalist Gasquet since 2004 and was sweet revenge for losing a Davis Cup quarter-final rubber to the French player in 2011 after being two sets to love ahead.
"It's an unbelievable feeling. Eight years ago I was here in the quarters, and now eight years later it's happened again. So it's a wonderful dream for me," said Mayer.
Ferrer never got the chance to start his match on Monday, but the 30-year-old, now carrying Spain's hopes after the elimination of Rafael Nadal, wasted no time against ninth seed Del Potro, racing home beneath the Centre Court roof in under two hours.
"Of course I prefer Rafael or another Spaniard here with me," said Ferrer, who is tied 5-5 in career meetings with Murray.
Kohlschreiber will face French fifth seed Jo-Wilfried Tsonga who reached the last eight for the third successive year by defeating American 10th seed Mardy Fish 4-6, 7-6 (7/4), 6-4, 6-4.
"He's a really great player. He's a big server, he has a huge forehand, so that's going to be of course tough to do something," said the German, who has defeated the Frecnhman just once in six meetings.
"But I'll try to keep him a little bit moving around, playing more to the backhand."
Tsonga needed treatment on a back injury at the end of the second set of a match which was twice stopped for rain after also being halted overnight on Monday with Fish in the ascendancy.