At a set and 5-1 down, the third seed looked in danger of suffering one of his biggest grand slam disappointments, but he turned things around and levelled the match on a tie-break.
That made Murray a big favourite and he reeled off 11 straight games to win 3-6 7-6 (7/4) 6-2 6-0 and set up a last-four clash against Tomas Berdych.
Murray had been due to play on the Arthur Ashe court at Flushing Meadows but the match was moved to the Louis Armstrong court because the earlier rain had put things behind schedule. This was the scene of Murray's third-round struggle against Feliciano Lopez, and the early signs were not good as the third seed won only one of the first 10 points, losing his serve to love.
The match had been displaying all the classic symptoms of an Andy Murray US Open upset. Until, that is, the Olympic Champion offered a swift diagnosis of the problem and set about making his opponent feel miserable instead.
Few people are more adept than the 25-year-old from Dunblane at analysing his own inadequacies, and in no time at all whatever remedy he had prescribed for himself had him feeling like his old self again.
The No 12 seed was vanquished as the Scot booked his place in his second successive US Open semi-final.
Remarkably that match, which will take place on Saturday, will be the Scot's eighth semi-final from the last 10 majors.
Murray admitted the going had got tough. "I've had a lot of tough matches - everyone goes through them. We've seen Rafa [Nadal], Novak [Djokovic] and Roger struggle here. There is pressure on you to perform well, expectations are high and sometimes you're nervous.
"I didn't start too well," he added. "He started off well. He was playing close to the baseline. I have always found that court tricky to play on. I have had a lot of tough matches on it. It's not that I don't like the court. Some great matches have been played on that court. I just haven't played that well on it. I'm just being honest.
"It took me a while to get used to it. But when the conditions slowed down a bit and started to get a bit darker, that helped me. When you play against guys of his size, you don't want to bring them necessarily into the net. Keeping the ball low is more important."
It is little wonder if Murray had begun this match a little under the weather. He was a victim of a day of intermittent drizzle in the New York area which caused havoc for the schedulers.
The sudden retiral of Stanislas Wawrinka against Novak Djokovic due to illness precipitated the shifting of the Scot from Arthur Ashe to the Louis Armstrong Stadium, the match beginning amid humid, sticky conditions, the venue less than half full.
But not only does the secondary court at Flushing Meadows play a lot quicker than Ashe, it is a far tighter arena and, to put it bluntly, during the first set Murray played like he didn't want to be there.
Cilic's wounding straight sets defeat of the Scot in 2009 had actually been played on Ashe, but this was a venue which doesn't always suit the Scot. He had lost to Nikolay Davydenko here on his first visit, succumbed in a bad one to Stanislas Wawrinka here, narrowly avoided defeat against Robin Haase of the Netherlands 12 months back, and been put through the wringer in his victory against Feliciano Lopez here on Saturday.
With Pippa Middleton in attendance, the Croat raced away to an early lead, breaking the Murray serve to love in the second game of the match, courtesy of a Murray double fault and then a backhand which flew long.
This was a different player from the one who produced a virtually error-free performance against Milos Raonic and, although he got his break back for 3-4, the Scot was unable to consolidate it, throwing his racket to the surface in disgust as he marched to his seat at 3-5.
The 23-year-old Croat held his nerve and his serve and the Scot was in trouble. This wasn't supposed to be in the script. Or at least, not the 2012 edition.
Things were to get worse before they got better. Two more double faults handed Cilic an immediate service break in the next set, and in no time at all that advantage had grown to 5-1.
But the Scot looked within himself and soon was moving better and feeling more comfort on the court. A charge to the net and cute drop volley was a sign that the match was turning, as Cilic twice faltered when serving for the set.
Soon we were into a taut second set tie-break - his fourth breaker of the tournament - which may well have determined the outcome of this match.
Errors were creeping into the Cilic game, two of which saw the Scot race into an early lead, but when the World No 4 missed an easy put-away he was up against it again at 2-4.
The Olympic Champion produced when it mattered though, denying the 23-year-old a single point more, and levelling matters up on the scoreboard when one last Cilic backhand struck the net. The neon also showed that the second set had taken just shy of one hour and 15 minutes.
Suddenly, seeds of doubt were germinating in the mind of Cilic, perhaps mindful of those previous defeats by Murray, including one at Wimbledon earlier in the year.
His serve was broken for 3-2, and after one fraught Murray hold, a cute backhand smash as both men went eye-to-eye at the net led to a second service break which gave the Scot a 5-2 advantage. The set was duly taken with an ace which Hawk-Eye showed to have clipped the line.
The World No 4 changed his white t-shirt for a slate grey one between sets and started the motor through the fourth, and on this occasion final, set. One of those brutal two-handed backhands which he loves to play gave him the first service break, a couple more aces flew off his racket, and before long he had broken to love for 3-0, and then for a third time for 5-0.
The Croat raged against the dying of the light long enough to force a couple of break points but the Scot was keen to deprive his opponent of the relief of a single game.
On match point, one last sweet backhand into the open court took him into his second semi-final here in successive years. He will take some stopping.
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