The British world number two ended the remaining home interest in the Grand Slam with a 6-4, 6-4, 7-6 (7/4) win over 16th-seeded Tomic to set up a last-eight match with Spanish baseliner David Ferrer.
Meanwhile, Canadian star Milos Raonic, who was also shaken in his previous match by a high school shooting in his home country, impressively ousted the 2014 champion Stan Wawrinka in a tense five-setter.
Raonic, bidding to broaden his game under new coach Carlos Moya, overcame the Swiss world number four 6-4, 6-3, 5-7, 4-6, 6-3 and will face Frenchman Gael Monfils in the last eight.
There were questions how Murray would respond in his first match after his father-in-law Nigel Sears, Ana Ivanovic’s coach, collapsed at the tournament and was taken to hospital on Saturday.
Sears was cleared to leave hospital on Sunday and fly home following tests. Adding to the tension of the moment, Murray’s wife Kim Sears is heavily pregnant and he has pledged to rush home if she goes into labour.
“Last few days were very, very tough. A lot of emotions, it’s been sort of changing all the time in my head,” Murray said on court moments after his win.
Murray put the medical emergency behind him but it was a scrappy match, as he broke Tomic’s serve six times and dropped his own serve four times.
“It was a tough match and both of us had our chances, Bernie didn’t play his best tiebreak and missed a few easy balls so that helped at the end but he fought right to the end,” Murray said.
Cut and bruises
Raonic, the Canadian 13th seed, came out on top of a tense five-setter with Wawrinka after letting slip a two sets lead.
It was Raonic’s first win against the reigning French Open champion in five meetings, and he has not lost a match at tour level since going down to Rafael Nadal in the third round of last year’s Shanghai Masters.
The power server, who beat Wawrinka’s fellow Swiss Roger Federer to win this month’s Brisbane International, was on track for a straight-sets win after four service breaks to lead by two sets.
But Wawrinka lifted his intensity and took the match to a fifth set.
“It’s the next step for me to try and achieve the goals I want to achieve and I am always looking at ways to get better and I am always working for that,” Raonic said.
Spanish eighth seed Ferrer ousted America’s John Isner in 6-4, 6-4, 7-5 in two hours, four minutes to set up his crack at Murray in the quarters.
Monfils said he was lucky not to break any bones after a trademark acrobatic dive left him with a deep cut and bruises on the way to his first Australian Open quarter-final.
The athletic Frenchman went airborne for an unsuccessful baseline volley during his four-set battle with Russia’s Andrey Kuznetsov.
Afterwards Monfils was left nursing a deep cut on his finger and bruising that left him unable even to hold a racquet — but he insisted he had no regrets about going for broke.
The 29-year-old won 7-5, 3-6, 6-3, 7-6 (7/4) in two hours, 37 minutes to reach the last eight and a tussle with Raonic for the first time in 11 attempts.