The top seeded Federer booked a semi-final against France's Jeremy Chardy with his imperious 57-minute 6-1, 6-1 win over an outclassed Matosevic.
Eighth seed Chardy had earlier downed another Australian, wildcard Sam Groth, 7-5, 6-4.
The second semi-final will be between second seed Kei Nishikori of Japan and crowd favourite Lleyton Hewitt.
Nishikori outlasted big-serving Croat Marin Cilic 6-4, 5-7, 6-2, while Hewitt was too good for Romanian qualifier Marius Copil, beating him 6-4, 6-2.
But all eyes were on Federer, who is playing in Brisbane for the first time in his career.
"Tonight I felt very good against Matosevic who can play very dangerously," said Federer.
"He's got a good enough serve and return as well. But I was able to control most of the match except the very beginning."
Nishikori and Cilic had to play in the heat of the day, but the Japanese world number 17 tamed the big-serving Croat in temperatures approaching 37 degrees Celsius, winning 6-4, 5-7, 6-2 in two hours, 37 minutes.
We played in tough condition: Nishikori
"It was hot — it was tough conditions, especially playing a one hour [first] set and almost two hours and 40 minutes," said Nishikori. "It was not easy, but I'm happy to finish strong in third set.
"He was a little bit dropping his level (in the third) I think, yeah, I'm very happy today."
Nishikori said he expected a tough battle against Hewitt.
"He's always tough to play — he doesn't miss much," said Nishikori of Hewitt.
"It's not easy [to play him] because he has decent serves and a good return and good backhand — very solid on groundstrokes."
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ