Murray, still feeling his way into the tournament following a hip injury, survived a scare against hot-headed Italian Fabio Fognini to win 6-2 4-6 6-1 7-5 in a gripping and fluctuating clash.
The world No 1 will be joined in the second week by Johanna Konta for the first time after the sixth seed dispatched Maria Sakkari 6-4 6-1 on Court One to show her credentials in a wide-open women’s draw.
The victories have heightened the prospect of a first British clean-sweep in the Wimbledon singles competitions of the open era.
However, that idea was in danger as Murray came under duress against Fognini.
The Italian, who had won three of the previous six matches between the pair, rattled Murray with his unpredictability and effortless forehand.
The Italian’s flamboyant character also led to him being penalised a point in the fourth set for a visible obscenity after sucking his fingers, having already been warned about his conduct after slamming his racket into the turf.
The incident appeared to throw Murray from his stride only for the Scot to regather himself as Fognini served to force a decider and he turned the set on its head to wrap up a dramatic victory in the dark.
Murray said: “It was a very up and down match. It wasn’t the best tennis; a little bit tense.
“I didn’t feel I moved as well as I did in the first couple of matches, but I’ve got two days to work on that. Hopefully I’ll come through that and play better tennis.”
Earlier, Konta needed little time to assert herself as she broke the serve of Sakkari in the opening game and served her way to the first set.
The second was a procession as Konta’s power game was too much for her Greek opponent.
Konta, who had previously won just once at SW19 prior to the 2017 Championships, has been installed as favourite for the women’s title by tentative bookmakers following the exits of Karolina Pliskova, and previous champion Petra Kvitova.
With each performance, Australian-born Konta is becoming a bigger favourite with the Wimbledon crowd.
On the favourites’ tag, Konta said: “I don’t spend too much time thinking about it or listening. Things move very quickly in tennis.
“I have said that everyone n the draw is in with a chance of taking the title. Favourites come and go and change daily. I’m just happy to make it to the second week.
“I think I am playing good tennis, but I don’t think I’m playing unbelievable tennis. I definitely believe I can improve and keep getting better.”
Konta will play in-form Frenchwoman Caroline Garcia in round four on Monday, a player who beat her in three tight sets at Indian Wells earlier this year.
“She is a very good player, playing with a lot of confidence,” Konta added. “I don’t anticipate anything other than a tough battle.”
Yesterday was the first time in 20 years four Britons have played in the third round.
But four became two as the home representation was halved by 3.30pm with Heather Watson and Aljaz Bedene bowing out on a sweltering day at SW19.
Watson, playing in the third round for only the second time in eight attempts at SW19, battled hard, but lost in three sets to former world No 1 Victoria Azarenka, twice a semi-finalist at Wimbledon
Azarenka has fallen to 683 in the world rankings after having a baby last year and only returned to the tour at the Mallorca Open last month. Watson, 25, had previously taken just 11 games from Azarenka in four meetings, but dominated the baseline exchanges to take the first set on Centre Court.
But her Belarusian opponent responded in the fashion of a double slam winner as her power stretched Watson’s defences and claimed the second set 6-1.
A hard-fought deciding set, which included three breaks of serve in succession, continued the attritional nature of the clash as Azarenka’s experience saw her through.
Bedene’s run, which had taken him to the third round for the first time, came to a halt in the opening match on Court Two.
Experienced grass-court specialist Gilles Muller, from Luxembourg, triumphed 7-6 (7-4) 7-5 6-4 against the the Slovenian-born British No 3.