Murray's consistency in the top tournaments is such that he has now reached the quarter-finals in each of his last 10 grand slam tournaments.
But Istomin, ranked 65th in the world, pushed Murray hard and the Wimbledon champion was glad to have made it through without a major scare.
"I was just very happy to get it done because he had chances at the end of the third set to get ahead," Murray said.
"But I'm in the quarter-finals of a Slam. That is not an easy thing to do and the matches are going to get tougher. I'll have to up my game," he said.
The Briton struggled to get out of the blocks in the first set and trailed 5-3 after two forehand errors handed Istomin the break in surprisingly cool and slightly gusty conditions.
Although Murray immediately broke back, he lost out in the tiebreak, with a double fault and a slice into the net allowing Istomin to serve out the set.
Istomin, decked out in luminous orange with similarly garish yellow-rimmed glasses, proved to be a determined opponent.
After levelling the match, Murray displayed some clear signs of frustration in the third set but finally took control by breaking Istomin in a marathon seventh game after the enterprising Uzbek had saved three break points.
There was never any doubt about who would win from then and the Scot wrapped up the match in a little over three hours.
Murray said the weather and wind in Arthur Ashe Stadium had been a factor in his slow start to the night match.
"It was extremely cold on the court, very windy. Often when you sort of heat up and then in between sets or if you have quite a long break, you cool down pretty quickly," he said.
"It was very, very different conditions to the last few days where it's been very humid and you have been sweating a lot," he said.
Istomin's decision to play the ball between his legs on three occasions, once when he had a perfectly playable shot, may have pleased the crowd but raised some eyebrows and surprised his opponent.
"I think it was 5-4 in the first set when he had a pretty easy shot. I personally wouldn't try something like that at that stage, but he did, and yeah, it was a bit surprising," he said.
Wawrinka, who beat Tomas Berdych on Tuesday, is up next for Murray and he knows he is in for a test.
"He has improved quite a lot this year, he has less weaknesses and is more experienced.
"He has a very good backhand, serves well, he's solid at the net and makes a lot of returns. He makes it tricky for you.
"He is a top player and it will be a very tough match for me," he said.
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