With the wind whipping the red clay into the air, Djokovic struggled with his serve and backhand in the opening set before settling down and wearing out Monaco.
"It was a very strange match. It was difficult to play with that wind but the conditions were the same for both us, he just handled it better at the start," Djokovic said, switching between Italian and English. "I was playing far too defensively and passively and he was controlling everything. He was the better player for a set and a half."
Federer also dropped a set in a 6-2, 5-7, 6-1 win over 2001 Rome winner Juan Carlos Ferrero. However, except for a brief lapse that resulted in a costly break at the end of the second set, Federer controlled play with expert serving and an array of winners on a cool and crisp evening with little humidity.
Federer hit 11 aces and led 46-12 in winners, closing out the match with a backhand overhead after following his serve to the net.
Federer won his 74th career title at the Madrid Open last Sunday, and improved to 47-3 since last year's U.S. Open final. He's won seven of his last 10 tournaments.
Earlier, Nadal routed Marcel Granollers 6-1, 6-1 and will next meet seventh-seeded Tomas Berdych, who eliminated Nicolas Almagro 7-6 (3), 6-3. Berdych was the runner-up to Federer in Madrid, where Djokovic and Nadal lost in the quarterfinals on the blue clay.
Murray skipped the Madrid Open with a back injury, and he said after the loss that it was still bothering him.
As for Djokovic, in the first set alone he committed 22 unforced errors -- 14 of which were backhands -- to Monaco's 16, and got in only 47 percent of his first serves.
When Djokovic missed two consecutive backhands to hand Monaco the first set, he slammed his racket to the clay twice, breaking it on the second attempt, which drew a warning from the chair umpire.
The burst of anger appeared to help, though, as Djokovic virtually eliminated errors from his game. He improved to 6-0 in his career against Monaco.
"It's not the first time and I don't think it will be the last time -- I'm a player with a lot of emotion," Djokovic said of breaking his racket. "I hope kids didn't see it. But then it changed the match. ... The momentum swung to my side."
Djokovic won this tournament for the second time last year, as part of his memorable 43-match winning streak.