Former world number one Djokovic has slipped six places to 18th after his second round defeat in Madrid, his lowest ranking since October 2006.
Novak Djokovic got off to a winning start in his bid for a fifth Italian Open title beating Ukraine's Alexandr Dolgopolov 6-1 6-3.
Looking for more wins, Djokovic awaits the qualifier battle between Nikoloz Basilashvili and Filippo Baldi.
Novak Djokovic eased into the second round of the Internazionali d'Italia on Monday with a straight-sets win over Alexandr Dolgopolov, as David Goffin and Kei Nishikori also won.
Djokovic kept the points short and sharp, mixing up his approach expertly and showing no signs of being troubled by his elbow as he broke for a 3-1 lead in the second set with a cross-court victor following another thunderous return. "I think the conditions are quite suitable to my game", Djokovic said.
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Two further break of serves enabled the 30-year-old to wrap up the first set in 20 minutes before Djokovic continued to keep the pressure on his opponent, who was broken twice more, as the former world No 1 celebrated victory after 55 minutes.
"Obviously I would like to go all the way but, at the same time, looking at my results I have to be a little more modest with expectations and see where it takes me". The bar has been raised so high.
"I know that I haven't been up to the level that I desired but I feel like my game has been going in the right direction in the last couple of tournaments".
Kei Nishikori edged by Feliciano Lopez in straight 7-6 (5), 6-4.
"It wasn't (an) easy match", Nishikori said.
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"The first set could have gone both ways, luckily I got it and after that I was more confident".
The pair exchanged serves in the second set before 2016 semi-finalist Nishikori broke again and served out to love to book his place in the second-round where he meets third seed Grigor Dimitrov of Bulgaria.
Wildcard Matteo Berrettini defeated Frances Tiafoe in straight sets and will now play Madrid victor Alexander Zverev, while 10th seed Pablo Carreno Busta needed three sets to see off Jared Donaldson.
Having already announced that this would be her final tournament, the 35-year-old Vinci was beaten by Serbian qualifier Aleksandra Krunic 2-6, 6-0, 6-3. Kohlschreiber came from behind to win the first set, but passed up on an opportunity to serve out the match in the second, allowing the Russian to force the decider. "Changes in general are good when they're focused on improvement and that's what I'm focused on and we'll see where it takes me".
Naomi Osaka, who claimed her first WTA title at Indian Wells in March, eliminated former No. 1 Victoria Azaranka 6-0, 6-3.
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American Madison Keys, seeded 13th, beat Russia's Anastasia Pavlyuchenkova 6-4, 6-1, with Britain's Johanna Konta easing past Slovak 17th-seed Magdalena Rybarikova 6-4, 6-3.