"One break was enough, 5-4, 6-5, both sets".
That set the tone for what proved to be the final set, Nadal providing answers for anything Goffin had to throw at him, and posing questions the world number 10 could not answer.
David Goffin awaits the victor of Nadal's clash with Australian Kyrgios as the Belgian beat world number six Milos Raonic 6-4, 6-2.
Nadal, a four-time champion in Madrid, had an easier time in the second set after earning an early break, and closed out the match with another at the end.
Almagro was two points away from going up 4-2 in the final set but was not able to capitalize on his chances. A Djokovic victory could prove to be a much-needed springboard for better results in the remainder of the season.
"Obviously when you're not winning too many matches, you have to build the confidence level", Madrid's second seed commented.
It was Djokovic, who had dominated on the clay a year ago as he went on to win the Roland Garros title.
Rafael Nadal is seeking his third consecutive clay court title after capturing the Monte Carlo Masters and Barcelona Open.
"I'm going to take a couple of days to see how the injury evolves but I hope to be in Rome". "I'm expecting the best Djokovic tomorrow".
"I think my backhand was good today and my forehand was there". As of now, there seems to be no stopping the tennis player, who is having a great time this year. Wednesday's match was his first since splitting with longtime coach Marian Vajda.More news: Paul Ryan: 'Rescue Mission' is Underway for Health Care
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Nadal was also taken to three sets before seeing off Fabio Fognini 7-6 (7/3), 3-6, 6-4.
Rafa held at love to move 5-2 ahead, leaving Nick to serve to stay in the set. He threw his racket on the ground three times in a row after losing a decisive point in the tiebreaker.
Nadal served first, racing to a 30-0 lead before Kyrgios made an early declaration of intent with a stunning two-handed return. The fifth-ranked Spaniard has won 22 of his last 24 sets. "I think Feliciano played really well, especially in the second set".
"My level of tennis was not so high today, but I managed to make it through the first round".
Nadal won 14 of their opening 18 meetings and looked as if he would dominate the duals between the two. "In his dip after Wimbledon, he won in Montreal. made the final at the US Open, the semi-finals in Shanghai, the final in the World Tour Finals".
Meanwhile, Djokovic advanced when Kei Nishikori withdrew before their quarter-final because of a wrist injury.
"It's been feeling good, better than I expected", Nishikori told the media in Madrid.
The other quarterfinal will be played between Pablo Cuevas of Uruguay, who defeated Benoit Paire of France 7-5, 0-6, 6-1, and Alexander Zverev of Germany, who beat Tomas Berdych of the Czech Republic 6-4, 6-4.
In the women's third round, Canadian Eugenie Bouchard had another victory as Angelique Kerber quit with a hamstring problem trailing 6-3, 5-0.
Mladenovic made it to her fourth final of the year_ and second consecutive _ by defeating Svetlana Kuznetsova of Russian Federation 6-4, 7-6 (4).