Despite the 7-6(1) 6-3 6-4 score line, it was not all smooth sailing against the burly Czech for the 36-year-old Federer.
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The 26-year-old Romanian world number one, still without a grand slam title, trailed 3-0, but battened down the hatches to reel off the next nine games on her way to a first Melbourne semi-final.
The South Africa-born 23-year-old Briton, playing in his first Grand Slam quarter-final, showed no nerves as he blazed away with his fearsome forehand to subdue a nervy Dimitrov.
The six-time champion had been playing in his first competitive tournament since a six-month injury layoff and at times, the former world number one looked to be struggling with an ongoing issue with his elbow.
The defending champion did not require his dazzling best in his first match scheduled during the day session but still emerged a winner.
The 36-year-old defending champion reached the fourth round of the Melbourne Park tournament for the 16th time by shifting up the gears when required to see off his French opponent in just under two hours on Rod Laver Arena.
The battle of the former champions ended 6-1 6-3 in Keber’s favour as the German progressed to the fourth round.
The Serb arrived in Australia with question marks over his elbow injury and has played two rounds in Melbourne wearing a compression sleeve on his serving arm.
Melbourne’s heat wave had relented by the time the 31-year-old Nadal walked on Margaret Court Arena, but the Spaniard was on fire as he battered the 28th seed into submission.
The 2009 champion again looked untroubled on Wednesday by his recent knee issues, claiming a 6-3 6-4 7-6 (7-4) victory in two hours and 38 minutes on Rod Laver Arena.
The 30-year-old former champion returned a positive doping test after a quarter-final defeat by Serena Williams in 2016, resulting in a 15-month ban from the sport.
The Serbian ace swung freely to amass 33 winners during the one hour and 51 minute rout at a sunbathed Margaret Court Arena.
Playing his first competitive match since pulling out of the ATP Tour Finals with knee trouble in November, the world number one showed no signs of early season rust.
The Swiss breezed through his media duties on Sunday with the same swagger he will take on court against Slovenia’s Aljaz Bedene on Tuesday, when he kicks off the defence of the title he won against great rival Rafa Nadal last year.
Williams said while she was close to regaining full fitness after giving birth to her first child in September, she was not fully ready to defend her title.
Williams has been in full training for just a month, though, and the 23-time Grand Slam winner has decided to delay her return to the big stage until she regains her sharpness.
The former No. 1-ranked Murray had been scheduled to play his first match at the Brisbane International on Thursday, but notified organizers he was pulling out after failing to practice on Tuesday.
“She’s got her visa, she’s entered, she’s practising and she’s probably just got to find a bit more space for a bigger entourage,” said Tournament Director, Craig Tiley
The Swiss ace has enjoyed a resurgent 2017, winning six ATP Tour titles, including two Grand Slam triumphs at the Australian Open and Wimbledon.
The 35-year-old discovered she was expecting shortly before the 2017 Australian Open in January but went on to win the tournament without dropping a set, beating her sister Venus in the Melbourne final 6-4 6-4