The Swiss served nine aces and broke serve five times in the pair's first meeting.
Federer, who is also through to the doubles semi-finals with Nicolas Mahut, is looking to win his 78th tour-level title this week.
On fire: Roger Federer raced to victory over Marinko Matosevic in the quarter-finals in Brisbane
Next he will face world number 34 Jeremy Chardy, who ended the run of Australian wild card Samuel Groth with a 7-5, 6-4 win in 69 minutes.
'I felt very good against Matosevic who can play very dangerous,' 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. For that, I'm very happy.'
Of Chardy, he said: 'He plays very aggressive on the hard courts.
Solid week: Federer is into the last four of both the singles and doubles events in the Queensland capital
'I remember seeing him play really well in Cincinnati, which is similar to here.'
Second seed Kei Nishikori set up a semi-final with home favourite Lleyton Hewitt.
The Japanese player edged Marin Cilic 6-4 5-7 6-2 to book a last-four meeting with Hewitt, who eased to a 6-4, 6-2 win over qualifier Marius Copil.
Rolling back the years: Former world No 1 Lleyton Hewitt has progressed to the last four in Brisbane
It is the second successive year
Nishikori has reached this stage but it was done the hard way, the match
lasting two hours and 37 minutes in scorching conditions.
Former world number one Hewitt, by contrast, took just an hour and 12 minutes to defeat Copil, who had upset Gilles Simon on Thursday.
Jamie Murray and Australian partner John Peers take on Mariusz Fyrstenberg and Daniel Nestor in the men's doubles semi-finals in the Queensland capital on Saturday.
Big match: Jamie Murray (right) and John Peers contest their men's doubles semi-final on Saturday
Stanislas Wawrinka earned his 300th win on the ATP tour on Friday as he breezed past Slovenian Aljaz Bedene 6-2, 6-1 to reach the semifinals of the Chennai Open.
Wawrinka became only the fourth Swiss player to reach the milestone after Federer (923), Marc Rosset (433) and Jakob Hlasek (432).
'I didn't know about it before coming here,' Wawrinka said. 'It's been a long time on the tour and it's amazing. For sure it's special. But I was focused on the match and knew that even if I did not get here I had a chance next week.'
The top-seeded Wawrinka needed little more than an hour to beat Bedene, who had ousted the Swiss player in the quarterfinals here last year in their only previous meeting on the tour.
Milestone: Stanislas Wawrinka picked up his 300th ATP tour win with victory over Aljaz Bedene in Chennai
Wawrinka started with a break and ran up a quick 5-0 lead in the first set. The 95th-ranked Bedene did manage a break in the sixth game but couldn't put up much of a fight the rest of the way.
'I'm very happy with the start this year, I feel very good,' Wawrinka said. 'Usually, I need a few tournaments but this time I feel good already.'
Wawrinka will next play fifth-seeded Vasek Pospisil of Canada, who beat local favorite Yuki Bhambri 6-3, 6-3.
In the other quarterfinals, seventh-seeded Frenchman Edouard Roger-Vasselin saved eight break points to beat Dudi Sela of Israel 7-5, 6-7(6), 6-0, while sixth-seeded Marcel Granollers of Spain ousted No. 4 Benoit Paire of France 6-2, 3-6, 7-6(5).
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