Murray returned at midday to finish off Croatian Cilic 7-5 6-2 6-3 in one of five men's fourth round ties unfinished because of Monday's rain.
The fourth seed, raising hopes of a first British male Grand Slam champion since 1936, was again held up by rain for a while but took advantage of a bright slot in the murky skies to dispatch Cilic with a minimum of fuss.
Murray will face Spain's David Ferrer in the quarter-finals in a repeat of their Roland Garros clash after the seventh seed thrashed Argentina's Juan Martin del Potro 6-3 6-2 6-3.
Florian Mayer and Philipp Kohlschreiber continued Germany's impressive showing at the tournament as they both reached the quarter-finals - matching the feat of Sabine Lisicki and Angelique Kerber in the women's draw.
Mayer finished off Frenchman Richard Gasquet 6-3 6-1 3-6 6-2 while Kohlschreiber ended the run of American qualifier Brian Baker to reach his first Grand Slam quarter-final.
Murray put his body and his fans through the mangle in the previous round against Marcos Baghdatis - a bruising, nerve-shredding encounter that ended at gone 11pm local time.
On that occasion a manic Murray played the last few games on fast forward as he raced to squeeze out a victory before the All England Club's cut-off time for night play.
Against Cilic, both on Monday when he established a healthy lead, and on the resumption on Tuesday on Court One he was unflappable, booming down aces and string the ball sweetly.
His only concern were the menacing rain clouds that threatened to clutter his schedule but even they held off to allow the fourth seed to reach the quarter-finals at Wimbledon for the fifth year in a row.
With his Wimbledon nemesis Rafa Nadal already sunning himself in the Mallorcan sunshine after his shock exit, Murray's path to the final is opening up but the Scot batted away suggestions that Ferrer, the less celebrated Spaniard, would be any less formidable away from his native claycourts.
"To me he's not a claycourt specialist," Murray, outplayed by Ferrer on the French Open dirt, told reporters.
"He won last week on grass, so he's won eight matches in a row on the grass."
Ferrer produced arguably the performance of the tournament to punish Del Potro - overcoming a huge height disadvantage with a jet-heeled display of relentless consistency that offered up only eight unforced errors.
The 30-year-old, who seems to be improving with age, has reached the quarter-finals here for the first time, becoming the sixth Spaniard to do so in the professional era.
Kohlschreiber will meet Frenchman Jo-Wilfried Tsonga in the other quarter-final in the bottom half of the draw after the fifth-seed, who defeated Roger Federer on his way to the semi-finals at the All England Club last year, beat Mardy Fish 4-6 7-7 6-4 6-4.
The match hinged on the second set tie-break when Tsonga warmed up the crowd with some inspired tennis to level on a cool and drizzly Court Two.
Tsonga saved break points before serving out the third set and then forged 4-2 ahead in the fourth before rain returned to halt his progress.
When the skies eventually lightened Tsonga knocked off the two games he needed.
Mayer will next face Novak Djokovic while the other quarter-final in the top half of the draw was determined on Monday when Roger Federer set up a last eight clash with Mikhail Youzhny.