Federer looked sharp in his Saturday afternoon match at Rod Laver Arena, serving for the second set after breaking Montanes in the penultimate game and then breaking again to open the third set.
"It was important to come through the first week," the Swiss star said. "I feel good, I feel confident. Physically I'm fine and mentally fresh and that's the way you want to go into the second week."
Australia's top player, former No. 1 Lleyton Hewitt, advanced when 2006 finalist Marcos Baghdatis had to retire with a right shoulder injury with Hewitt leading 6-0, 4-2 in a night match at Rod Laver Arena.
The last time the pair met here, they started just before midnight and concluded the match -- won by Hewitt -- at 4:34 a.m. Hewitt now plays Federer in the fourth round.
This Hewitt-Baghdatis rematch lasted just 54 minutes.
"I just said to him, 'mate you've got a lot of ticker [heart] to come back like you did today," Hewitt said he told Baghdatis when the Cypriot player came to the net to retire.
Baghdatis had clutched his shoulder during changeovers and motioned to his coach that he was having difficulty breathing due to the pain.
"I just feel some pain on the shoulder ... I couldn't hit the forehand," Baghdatis said. "I couldn't control the ball. I didn't think that it would be this painful during the match."
Federer has plenty to play for -- he'd like to win his fourth Australian Open title and walk away from Rod Laver Arena on Jan. 31 without tears in his eyes, as he had last year when he lost to Rafael Nadal in the final.
Federer spoke Saturday about his mental toughness, which he said is needed to "stay at the top of the rankings for so long."
"Victories don't come easy," Federer said. "I had to battle through, and there was tough moments and frustrating moments out there. You have to be mentally strong to be at the top no matter, regardless of the player you are."
Federer then spoke about Nadal, who plays his fourth-round match Sunday against Ivo Karlovic.
"With him, it's from point one to the last point it's always the same intensity," Federer said. "He never drops it."
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, and his best runs at a major ended in semifinal defeats at the French and U.S. Opens.
Djokovic took a while to get untracked in his second-round match when he dropped the first set against Marco Chiudinelli. But Djokovic was in command from the start Saturday against Istomin.
Djokovic, who won his first and only Grand Slam title at Melbourne Park two years ago, will play Poland's Lukasz Kubot. Kubot received a walkover in his third-round match when his opponent, Russia's Mikhail Youzhny, withdrew because of a right wrist injury.
Information from The Associated Press was used in this report.