However, he insists there were positive to take from his brief time in Madrid.
Milos Raonic defeated Nicolas Kicker 6-3, 6-2 to set up a second-round encounter with third-seeded Grigor Dimitrov, while Richard Gasquet beat Tomas Berdych 6-4, 6-2 to advance to play qualifier Dusan Lajovic, who got past Karen Khachanov 6-3, 6-2.
Djokovic was ready to pounce though early in the second and opened up a 2-0 lead.
It was Djokovic's first victory over a top-20 opponent since the Serb overcame Monfils at Eastbourne in June. "But, also, he was courageous enough to attack the balls when it mattered and deserved to win", Djokovic said.
"So that's why it was really a ideal scenario to start off the tournament". I guess I've had a better win on paper. Nadal's defence of his title began in comfortable fashion as he coasted to a 6-3 6-1 win over France's Gael Monfils yesterday.More news: Indian refiners in no rush to seek alternatives to Iranian oil
Frenchman Lucas Pouille, seeded 15th, crashed out of the tournament after a 6-2 6-3 defeat by compatriot Benoit Paire.
Maria Sharapova, who won in Madrid in 2014, made it to the round-of-16 by defeating Irina-Camelia Begu 7-5, 6-1 in only her second match since the Australian Open.
Barty, 22, was ultimately let down by her groundstrokes in crucial stages of the decider, finishing with 54 unforced errors.
Edmund moves on to face eighth-seeded David Goffin in the third round.
"It was a lot of hard work", Sharapova said of her match. She loves the clay. "That's where I draw my strength". It's just about going for it again. But it just shows even though I'm playing at a better level this year, you still lose. So does me the world of good in lots of ways: confidence, belief.More news: Of Rihanna's Best Fashion Moments At The Met Gala
"I think there's more people that have an opportunity here on this surface". Another break at 4-2 meant the match would be settled in a third set.
However, the Czech broke serve in the 11th game to win a tense battle. The former world number 7 is looking to make it to the top and if he is to do that, these are tournament that he must win.
David Goffin has had a very solid 2018 and is coming off a strong tournament in Barcelona where he lost to Rafael Nadal. Obviously, I've played this sport for so many years and had a bunch of success.
"Well, at the end of the day when Djokovic plays, normally he's always favourite. It does me the world of good".
"At the same time, you know, nobody is forcing me to play this sport. That will certainly help me moving forward".More news: Top Chinese economic adviser to visit USA next week for trade talks
The final quarter-final will be between second seed Alexander Zverev - a 6-4, 6-2 victor over Leonardo Mayer, and John Isner, who edged Pablo Cuevas 6-7 (9), 7-6 (3), 7-6 (4).
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