On the eve of the 10th anniversary of his first title at the All England Club, Murray rolled back the years with a performance showcasing all his famous grit, skill and grass-court nous to lead 6-7 (3) 7-6 (2) 6-4.
There were boos when it was announced the match would be halted with 20 minutes still to go until the 11pm curfew but Murray was probably not too disappointed after a hugely concerning moment at set point when the Scot screamed in pain and fell to the ground clutching his left groin.
Mercifully he quickly got to his feet and clinched the set with a serve that drew a Tsitsipas error, and the hope must be he has not done anything that could jeopardise his chances.
The match did not begin until gone 7.30pm, mostly as a result of the win of Broady’s life, with the 29-year-old outlasting world number four Ruud to clinch a 6-4 3-6 4-6 6-3 6-0 victory.
The win over Ruud, who has made the finals of Roland Garros and the US Open during the past 12 months, was even sweeter for the Stockport left-hander given it took place in front of a buoyant Centre Court crowd.
“It was a pretty terrifying, exhilarating experience coming out at Centre Court on Wimbledon, but it’s been my dream since I was five-years-old,” said Broady.
“I played on Court One in the finals of the juniors (in 2011). I was a set and a break up. I completely choked it, completely guffed it. That has kind of haunted me my entire career, to be honest.
“It always bothered me coming back, playing on the bigger courts and never really feeling like I was comfortable and had performed. That’s why it felt good. I feel like it’s taken a monumental effort for me personally to be able to win a match on Centre Court at Wimbledon.”
Like Broady, British number one Boulter is through to the third round for the second consecutive year after a 6-0 3-6 6-3 win over Viktoriya Tomova, and will meet last year’s winner Elena Rybakina.
“I think it’s a super great opportunity for me,” she said. “I’ve got nothing to lose. She’s clearly the defending champion for a reason.
“I’m going to have a swing and go for it. I’ve got a lot of tennis behind me. It’s time for me to test my skills against an incredible champion. I think I’m playing really well. I feel very comfortable.”
Jan Choinski was the only British singles player to lose, the German-born 27-year-old going out 6-4 6-4 7-6 (3) to his former junior doubles partner Hubert Hurkacz.
Choinski hopes to improve his ranking enough to earn direct entry in 12 months’ time, saying: “I would be very happy coming back next year. Maybe even without needing a wild card for the main draw, try my best to get my ranking to a position where I can enter the tournament by myself.”
Qualifying has been impacted at the year's first grand slam due to poor air quality, with organisers facing criticism for letting play go ahead despite the conditions.
Slovenian Dalila Jakupovic retired during her match due to breathing difficulties, with the air quality in Melbourne in the 'very poor' range on Tuesday as smoke from bushfires in Australia cause havoc.
Broady, who was beaten in qualifying on the same day, hit out at organisers amid concerns over player welfare.
"The more I think about the conditions we played in a few days ago the more it boils my blood. We can't let this slide," the Brit wrote in a message posted on Twitter.
"The email we received yesterday from the ATP and AO was a slap in the face, conditions were 'playable'. Were they 'healthy'? Citizens of Melbourne were warned to keep their animals indoors the day I played qualifying, and yet we were expected to go outside for high intensity physical competition?
"What do we have to do to create a players union? Where is the protection for players, both male and female? When multiple players need asthma spray on court and they don't even have asthma? When a player collapses and has to retire due to respiratory issues?
"On tour we let so many things go that aren't right but at some point we have to make a stand. ALL players need protection not just a select few."
Conditions in Melbourne improved on Wednesday, although 'moderate to poor' air quality was forecast for Thursday.
Seven-times grand slam doubles champion Murray was asked about the decision to grant Djokovic a medical exemption for the year's first grand slam tournament at Melbourne Park.
Players have been obliged to either prove they are vaccinated against COVID-19 or apply for an exemption, which tournament organisers said involved a "rigorous" process to prove eligibility.
World number one Djokovic is a nine-time Australian Open men's singles champion, yet it was unclear until Tuesday whether he would be allowed to play the event this year.
There has been early backlash to the decision to clear him, with Melbourne having been hit by multiple lockdowns during the pandemic and many believing only vaccinated players should be playing.
Murray, brother of Djokovic's long-time friend and rival Andy Murray, spoke after the Serbian was permitted to travel into Australia and said he doubted he would get the same treatment.
Asked about the situation in an ATP Cup news conference, Jamie Murray said: "I don't know what to say about that really. I think if it was me that wasn't vaccinated, I wouldn't be getting an exemption.
"But well done to him for getting cleared to come to Australia and compete."
Djokovic may wish to elaborate further on the factors behind him being given the green light to travel into the state of Victoria, and will doubtless face media questions about the situation once he arrives.
However, the 20-time grand slam winner has been unwilling to disclose his vaccination status until now, which suggests there is little prospect of him offering further medical insight at this stage.
Asked if he felt it was not a fair decision to exempt Djokovic, Jamie Murray added: "Whatever you want to say, that's the situation."
Murray, 35, was interrupted at that point by Great Britain captain Liam Broady, who said: "At the end of the day, you have to trust he has a valid reason for the medical exemption, that's all you can say about it really, isn't it."
However, Broady had no doubt Djokovic would play the Australian Open, which begins on January 17, and claimed it was a foregone conclusion.
In an Instagram story, Broady posted a screenshot of Djokovic's announcement, adding the remark: "The second AO announced there would be exemptions 8 weeks ago we all knew."
Murray has not played in a tournament since losing to Andrey Rublev in the second round in Rotterdam in March due to a groin injury.
The three-time grand slam champion flew to Rome to step up his preparation for a return, practicing with world number one Novak Djokovic and Diego Schwartzman on Sunday.
Murray will also make an unexpected doubles appearance, partnering fellow Brit Broady at the Foro Italico after Hubert Hurkacz and Felix Auger-Aliassime withdrew.
They will face Australian duo Max Purcell and Luke Saville for a place in the second round in the Eternal City on Wednesday.
Murray has entered qualifying for the French Open as he waits to discover whether he will be handed a wildcard for the second major of the year, which starts on May 30.
The former world number one is also hoping to receive a wildcard to play in Geneva or Lyon next week.
Scot Murray confirmed on Monday he will play at the Queen's Club Championships in June.
In his first competitive action since appearing at the Davis Cup Finals in November, the three-time grand slam winner recorded a 6-2 6-2 win over Liam Broady on Tuesday.
Murray admitted beforehand that he had little chance to practice before taking part in the exhibition tournament at the National Tennis Centre in Roehampton, stating before his opener that his main aim was to "get through" it with his body holding up.
The Scot has been troubled with a pelvic injury but, with his serve working well and showing the occasional glimpse of his undoubted quality, he proved far too strong for Broady.
Still, he refused to get too carried away with his performance, describing it as "okay" during his post-match interview with Amazon Prime Video.
"I served pretty well, I thought I served well throughout the match. A lot of free points there – I've been working on my serve quite a lot," Murray said.
"I didn't hit the ball that well from the back of the court, quite a lot of errors and my balance didn't feel great. I wasn't timing the ball very well, but it was alright.
"For a first match in seven months, I've not been practising much and not even doing that well in practice matches, it was alright."
However, Murray is expecting to have problems on Wednesday when he attempts to deal with Edmund, who began his campaign by beating James Ward.
"He's fit, hitting a big ball, so I'd be surprised if I manage to come through that one," the world number 129 said of his next opponent.
"If I serve like I did today and hit the ball better a little bit cleaner from the back of the court, I'll give myself some chances. But it will be tough."
The event, organised by Jamie Murray, is following strict health guidelines as it is taking place amid the coronavirus pandemic.
Rune – the fifth seed for the tournament in Bulgaria – required two tie-breaks to clinch victory in his first meeting with Van Rijthoven on the ATP Tour, eventually claiming a 7-6 (7-2) 7-6 (8-6) win.
After the match, Rune expressed his relief at avoiding a third set, saying: "I didn't want to go to three sets. If it [had happened], I was going to fight for sure and try to take it in three, but I'm very happy to finish in two."
Meanwhile, eighth seed Oscar Otte beat Dragos Nicolae Madaras 6-3 6-2, and Portugal's Nuno Borges overcame Mirza Basic in three sets to tee up a meeting with defending champion and top seed Jannik Sinner.
In Tel Aviv, seeds Aslan Karatsev and Tallon Griekspoor fell at the first hurdle with three-set reverses to Tomas Martin Etcheverry and Vasek Pospisil, respectively.
Etcheverry rallied after Karatsev took a second-set tie-break in comprehensive fashion to post a 6-2 6-7 (0-7) 6-4 win, while lucky loser Pospisil stunned Griekspoor for a 4-6 7-6 (7-3) 7-5 triumph.
Fifth seed Botic van de Zandschulp fared better, however, dispatching Joao Sousa 6-2 6-3 after producing a top-class display of serving.
The Dutchman will meet Britain's Liam Broady in the next round after he recorded a straight-sets win over Hamad Medjedovic.
