Play under the floodlit Centre Court roof cannot go past 11pm under an agreement with local residents, and the clock struck 11 as Murray took a 5-1 lead in the fourth set.
However, the Scot was allowed to serve out the match, giving him a day off ahead of his last 16 encounter with Marin Cilic on Monday.
Murray said: "I was under the impression that at 11pm we were stopping regardless of what the score was, and I think I actually broke serve to go 5-1 at that time, and then walked to the net because I thought we were going to have to come back on Monday."
The fourth seed beat Baghdatis 7-5 3-6 7-5 6-1, and said he needed to step up his level in the second week.
"I was very nervous, I knew it was going to be tough," said Murray.
"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."
Murray also insisted he was not thinking about the final, after his predicted semi-final opponent Rafael Nadal was shocked in the second round.
"As a player you are always conscious of what is going on around you in the draw but the draw didn't open up for me," he said.
"The draw opened up for Philipp Kohlschreiber and the guys that are in that part of the draw.
"If I get to the semi-finals then yes that will help, but it's silly for me to think Nadal's out so therefore I am guaranteed a place in the final - that's definitely not the case at all. I have got to keep my head focused on my next match."