Less than 48 hours after rushing to hospital to visit his father-in-law Nigel Sears, Murray produced a professional performance on Rod Laver Arena to beat Tomic 6-4 6-4 7-6 (7/4).
The world number two will now play eighth seed David Ferrer for a place in the semis, after the Spaniard had earlier knocked out John Isner in straight sets.
“It was a tough match, both of us had our chances,” Murray said.
“He fought to the end but I made a few more balls. It was a scrappy match, there wasn’t a period where we were both playing our best, it was up and down.”
Murray had never dropped a set to Tomic in the pair’s three previous meetings but a question mark surrounded his focus after the unnerving events over the weekend.
The Scot was far from his free-flowing best but this was a gutsy display against a player ranked 17th in the world and with ambitions of making the top 10.
The pattern was set in the very first point as Tomic followed a blasting forehand into the net, only for Murray to rip a backhand pass that was too hot for the Australian to handle.
Murray’s defence was typically strong and Tomic was left applauding when a 32-shot rally ended with the Scot digging out a stunning backhand winner.
His attacking instincts, however, were off and his first-serve percentage was less than 60 per cent, meaning he had to work hard to shade a frenetic opening set.
Five breaks from 10 soon became eight from 13 as all three games at the start of the second set went the way of the returner.
Murray, however, was again one up and that was how it stayed until 5-4 when he served out with an ace for a two-set lead.
Tomic stuck to his approach of all-out attack but it was yielding more unforced errors than winners and when another forehand flew wide, Murray was gifted another break early in the third.
It felt like the end might be just around the corner but Tomic sparked hopes of a comeback as he broke Murray’s serve then held his own to love to lead 4-3.
The youngster was swinging freely and rushing the net with even more regularity and it worked as he survived some intense Murray pressure to force a tie-break.
At the crucial moment, however, Tomic faltered as he missed two simple forehands to trail 2-1 when he should have been up 3-0.
Murray never looked back and with four match points, he converted the third as a forehand long sealed the Briton’s victory in two and a half hours.
The former world number one, seeded 14, proved too strong for Czech Barbora Strycova on Rod Laver Arena, storming through 6-2, 6-4 to set up a last-eight clash with the seventh seed, who beat fellow German Annika Beck 6-4, 6-0.
Azarenka, who won at Melbourne Park in 2012 and 2013, has a 6-0 record over Kerber, including in the Brisbane International final this month, making her a hot favourite to keep her run for another title going.
“I’m looking forward to it. She’s such a fighter and such a nice person,” said the Belarusian, looking ahead to the test on Wednesday. “I’ll just give it my best and I’m sure she’ll do the same.”
Kerber powered past Beck to reach the quarter-finals for the first time and knows she has a formidable task ahead against a player who has won each of their encounters dating back to 2012.
“I had tough matches against her in the past. I never won against her right now, but that will be a challenge,” she said.
World number one Serena Williams and fifth seeded arch-rival Maria Sharapova play each other in a headline last eight clash on Tuesday, while fourth seed Agnieszka Radwansa faces 10th seed Carla Suarez.
The final two players in the quarters will be determined later Monday when American Madison Keys squares off against Chinese qualifier Zhang Shuai and British hope Johanna Konta plays Russia’s Ekaterina Makarova.
Azarenka, 27, has been in the zone at Melbourne Park, dropping just 11 games in four matches as she zeroes in on a return to the top after battling injuries for the past two years.
It means she will also be missing Romania’s Fed Cup tie next week.
Halep was crashed out of the Australian Open in the first round to Chinese qualifier Zhang Shuai last week and revealed she had been struggling with nose, ear and stomach infections.
“The last six weeks have been extremely difficult for me, as I’ve been dealing with infections in my stomach, nose and ear,” she said on her official Facebook page.
“This has been one of my most frustrating periods, as I’ve not been able to train or stay healthy even though I’ve constantly been on antibiotics to help clear the infections.
“I gave it my best shot in Australia but, with the infections still in my body, unfortunately I made things worse, as I pushed myself to compete and fight in a Grand Slam.
“Under doctors advice, I will undergo surgery to fix the ongoing problem with my nose – and I’ve been advised that this is my best option and success is highly likely.”
She said she hopes to be back to defend her Indian Wells title in March but will miss Romania’s Fed Cup tie against the Czech Republic.
“It comes with great sadness that I’m announcing that I will need to miss our upcoming Fed Cup tie next week, as I will be undergoing surgery this week,” she said.
“I’m hopeful that I will have recovered in time to have a chance to defend my title in Indian Wells.
“But I will take it slowly and make sure that I am back to full health before resuming training and competition.