The Scot battled his way past the dangerous Marcos Baghdatis late Saturday, edging a 7-5, 3-6, 7-5, 6-1 win in three hours and 13 minutes just in time for the 11:00 p.m deadline imposed on matches for health and safety reasons.
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 realised.
"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 Centre 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, fuelling further concerns about his fitness.
"My knee was a little bit sore," he told the BBC. "I took a tumble towards the end of the second set, I slipped and my foot went from underneath me and when I cooled down a little bit, when we had the break with the roof, it was a little bit stiff.
"I had the physio work on it and put some tape on it and it was ok.
"I was struggling quite a bit with my footing early on, I changed shoes as well during the break and that helped."
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.
"It was annoying and it lost me two points so I need to make sure I have no problems with that during the next few rounds."
The next opponent for Murray is 23-year-old Croatian Marin Cilic with their match scheduled second up on Court One on Monday. There was no play scheduled for Sunday at Wimbledon as is the tradition.
Cilic made it through by defeating Sam Querrey 7-6 (8/6), 6-4, 6-7 (7/2), 6-7 (7/3), 17-15 in what was the second longest match in Wimbledon history.
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, and he said: "It will be important for me to try to get off to a good start. If you are feeling a little bit tired and you go behind, it can be tough to come back."
Murray was due to practise later Sunday and return to Wimbledon for the Cilic clash on Monday although there was rain in the forecast.