The pair, who are both regarded as two of tennis' biggest legends, share a competitive, but friendly, rivalry, but Federer is sure to be gutted at losing his status as the world number one.
It was an impressive performance from the 30-year-old in his first match since splitting from coach Andre Agassi and starting to work again with long-time former coach Marian Vajda.
Now, the world number one is back in Monte Carlo where he has amassed an incredible win/loss record of 63-4, winning ten titles from his 11 finals.
"I've had a very hard time in the last 12 months with the injury and everything else that's happened".
Quizzed on whether he was anxious about suffering another setback when he returns to the ATP Tour at the Monte Carlo Masters in the coming week, Nadal said: "Well it happened twice so you never know".
"Being in Monte-Carlo always gives me the best feelings possible and good memories".
"I feel that I'm playing well".
Over the course of the near one-hour match, Djokovic kept compatriot Lajovic guessing with his disguised forehand drop-shots and powerful down-the-line backhands that brought rapturous applause from the crowd at the show court. Third seed Alexander Zverev, unseeded Kyle Edmund, and Denis Shapovalov are some of the young names, who can reach the final stages of the clay-court tournament. He has not won a Grand Slam tournament since the 2016 French Open.
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"It's not great but, I mean, first match on clay, you know, I'm expecting (a) little soreness", said Nishikori. I always enjoy this Europe season.
'I'm looking to having good days of practice before the tournament starts and when the competition arrives I will be ready for it'.
The 28-year-old, who is making his first Monte Carlo appearance since 2012, will face Russian Daniil Medvedev in the next round.
Elsewhere, American Jared Donaldson launched into an angry tirade at umpire Arnaud Gabas while squaring up to the Frenchman over a line call during his defeat by Albert Ramos-Vinolas.
This will be his first meeting against the 21-year-old Khachanov, who is ranked No. 40.
To say Donaldson was unimpressed with Gabas not calling a Ramos-Vinolas serve out would be an understatement, as he confronted the French official before calling for a supervisor.
This is published unedited from the PTI feed.