Defending champion Federer, battling a flu bug according to the local media, was made to work hard by his Bulgarian opponent before the Swiss master prevailed 6-4 6-7(4) 6-4 at the Pat Rafter Arena.
"It was tough. Grigor's a great shotmaker, the future's ahead of him in the game," Federer said after setting up a semi-final against Austrian youngster Dominic Thiem.
Federer broke Dimitrov in the 10th game to claim the first set but the Bulgarian refused to throw in the towel.
For the first time in his four meetings with the world number three, Dimitrov managed to win a set via a tiebreak to force the decider but could not pull off an upset.
"The third was close and thankfully I started to serve a little bit better," Federer said.
"Maybe he didn't have his best finish of the match today, but I enjoyed it anyway."
Eighth seed Thiem made it through to the semis by beating former U.S. Open champion Marin Cilic 2-6 7-6(4) 6-4, while home hope Bernard Tomic continued his promising form by overcoming Kei Nishikori.
Tomic prevailed 6-3 1-6 6-3 against 2014 U.S. Open runner-up Nishikori.
"Obviously this win is huge," the world number 18 said after taking out the second seeded Japanese to set up a semi-final against big-serving Canadian Milos Raonic.
"Now I'm at the level the last few months of being in the top 20 and playing these players that have been consistently in the top 10, five in the world."
"Being in the top 10. It's near. If I keep playing the way I'm playing there is a chance."
The Australian, who has been criticised for poor behaviour in the past, went from 78th in the world to his current career-high last year when he claimed a third tour title in Colombia.
Raonic will provide another stern examination of those top-10 credentials after the Canadian easily took down France's Lucas Pouille 6-4 6-4.
(Writing by Patrick Johnston in Singapore and Amlan Chakraborty in New Delhi; editing by Toby Davis)
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