The Scot battled his way past the dangerous Marcos Baghdatis late Saturday, edging a 7-5, 3-6, 7-5, 6-1 win in 3 hours 13 minutes.
It was the latest-ever finish at the All England Club.
And while the victory kept alive his hopes of finally winning a Grand Slam title at the age of 25, Murray said he was aware he had to find another gear if that dream is to be realized.
"I was very nervous, I knew it was going to be tough," said Murray of the win over Baghdatis.
"I was just kind of hustling my way through the match and I am going to need to play better, if I want to go deep into the tournament.
"I was really struggling. Even in the first couple of sets I was creating lots of chances but I was not feeling that comfortable on the court."
There were concerns also over Murray's fitness as he took several painful-looking tumbles in a Center Court match that saw the sliding roof closed at the start of the third set.
Murray returned to the court after the break, while the roof was closed, with his knee strapped up, fueling further concerns about his fitness.
Oddly Murray also had problems with his shorts, suffering a two-point penalty because the ball fell out of his pocket during play.
"It's happened before but not like that, it happened like five times in all," he said. "I'm blaming the shorts though, it wasn't my fault."
Murray leads their head-to-head rivalry 5-1, the only win for Cilic coming in the last 16 at the 2009 US Open. The Scot got his own back the following year when he beat Cilic to reach his first Australian Open final.