Top seeded Federer is on the march to retrieve title honours after losing a tight final one year ago to Rafael Nadal. Victory over the 32nd-ranked Montanes nudged Federer's career mark at Melbourne Park to 50 wins, seven losses.
Federer's performance was flawless, with nine aces and 42 winners. He broke Montanes three times and never faced a break point in the easy outing.
The world number one finished with a forehand winner into the corner after less than two hours.
"He's tough, I've played on him on clay," Federer said. "I expected him to miss more on this faster court.
"I had to serve well, if I had any hiccups on serve it could have been a close match. I'm happy to be through of course.
With his own win wrapped up by mid-afternoon, the Swiss world number one had the chance to relax as Lleyton Hewitt and Marcos Baghdatis did battle at night for the right to face Federer in the next round.
Hewitt, a 2005 finalist and Cypriot Baghdatis both have a proud Melbourne history, with Hewitt winning a third-round match at the event in 2008 which did not end until 4.30 a.m.
Baghdatis is a darling of the large Cypriot community in multi-cultural Melbourne since losing the 2006 final to the Swiss. Should Federer face Hewitt, it will be the 25th meeting between the all-star pair in a rivalry dating back 11 years.
Poland's Lukasz Kubot marked the most successful Grand Slam appearance of his career as he advanced when Russian Mikhail Youzhny withdrew before their match due to a right wrist injury.
Nikolay Davydenko, Federer's potential quarterfinal opponent, extended his impressive winning run with a 6-0, 6-3, 6-4 victory over No. 30 Juan Monaco of Argentina.
Davydenko will next face Fernando Verdasco, who lost an epic, five-set semifinal to eventual champion and fellow Spaniard Rafael Nadal last year. Verdasco advanced when Austria's Stefan Koubek retired due to a virus after losing the first set 6-1.
The sixth-seeded Davydenko counts wins against Federer and Nadal at last year's World Tour Final and this season's opening event at Doha among his 12-match winning streak. The 28-year-old Russian has never gone beyond the quarterfinals at the Australian Open.
Novak Djokovic, who beat Federer in the semifinals en route to the 2008 title here, had a 6-1, 6-1, 6-2 win over Denis Istomin of Uzbekistan.
Serena Williams advances
Four women's seeds led by holder Serena Williams all went through into the second week of the major.
Top seed Serena Williams was untroubled by Spain's Carla Suarez Navarro 6-0, 6-3 while seventh seed Victoria Azarenka of Belarus defeated Italian Tathiana Garbin 6-0, 6-2.
Russia's ninth seed Vera Zvonareva beat Argentine Gisela Dulko 6-1, 7-5 while 13th seed Samantha Stosur kept Australian hopes high as she defeated Alberta Brianti of Italy 6-4, 6-1.
Last year, Suarez Navarro beat Venus Williams in the second round and made it to the quarterfinals.
The Spaniard didn't even get close this time, and the Williams sisters remained on course for a semifinal meeting when Venus held off Australia's Casey Dellacqua 6-1, 7-6 (4), closing with an ace on her fourth match point.
Serena Williams' only real difficulty was in closing the first set, needing eight set points in a game that went to deuce 13 times and lasted longer than the previous five games combined.
After she missed her seventh set point, pushing a backhand too long, she dropped into a sitting position on the court with a look of disbelief on her face.
"It was definitely the toughest 6-Love set," she said. "I thought, 'OK, Serena, don't put too much pressure on this. Worst case scenario it will be 5-1. But way to keep fighting."
Women's No. 1 Williams, who has won the Australian title each odd-numbered year since beating sister Venus in the 2003 final, will next play No. 13 and local hope Sam Stosur, a 6-4, 6-1 winner over Italian Alberta Brianti.
Venus will play No. 17 Francesca Schiavone of Italy, who ousted No. 10 Agnieszka Radwanska 6-2, 6-2.
"Of course I want to progress well to the final, that is my goal," said Venus, who lost the 2003 title match here to her sister. "So far, I'm getting closer. You know how it works. Just got to play well every match."
No. 7 Victoria Azarenka of Belarus had a 6-0, 6-2 win over Italy's Tathiana Garbin to set up a fourth-round match against No. 9 Vera Zvonareva of Russia, who beat Argentina's Gisela Dulko 6-1, 7-5.
China's Li Na equaled her best run at Melbourne Park when she advanced 7-5, 3-6, 6-2 over 2008 semifinalist Daniela Hantuchova. Li is only one win away from reaching the quarterfinals at a third major.