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.
In terms of head-to-head matches, Murray leads Ferrer 12-6, with the Scot winning the last five.
“It was a tough match, both of us had our chances,” Murray said.
“In the tie-break Bernie didn’t play his best, he missed a few easy balls which helped when I was a bit nervous.
“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.
Sears, who collapsed in the stands while watching his mentee Ana Ivanovic, was given the all-clear to fly home on Sunday, but the disruption to Murray’s preparation and mindset might understandably have affected his tennis.
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 last few days were very tough, a lot of emotions,” Murray said.
“Things were changing all the time in my head, it’s been a stressful few days.
“It was good to get through today, I’ll just try to relax now and get ready for the next one.”
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 other quarter-final matches see Novak Djokovic take on Kei Nishikori; Roger Federer meets Tomas Berdych and Gaels Monfils faces Canadian Milos Raonic.
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