Rain in the Spanish capital meant the roof on the Manolo Santana court was closed for the game, slowing down the powerful serve of Lopez to the advantage of the Serb, who recently split from his long-term coach Marian Vajda.
Nadal begins his quest for a fifth title in Madrid later Wednesday against Italy's Fabio Fognini.
Playing his first match after firing his whole coaching staff, Novak Djokovic struggled.
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.
"I think if he continues playing as he's been playing today and winning matches, it'slogical we're going to see the same Djokovic as we're used to seeing".
The early signs were positive for the 12-time Grand Slam champion as despite losing his service in the opening game, he broke straight back to start a six-game streak to romp through the first set. He was beaten by qualifier Denis Istomin in the second round of the Australian Open.
He was broken three consecutive times in the first set, and once in the second to give Coric a 5-3 lead that he converted to close out the match.
Curling a running forehand victor, Lopez issued a love hold for 3-all. I want to fight again in every match'.
Play starts for the Madrid Masters quarter-finals at 12pm (11am BST).
Eighth-seeded Dominic Thiem of Austria joined him by defeating Jared Donaldson of the United States 6-3, 6-4 - while ninth-seeded David Goffin had nine aces on his way to a 7-6 (3), 6-0 win over Florian Mayer. However, the tables have turned this season as Nadal has looked unstoppable on his favourite surface, winning his 10th title at Monte Carlo Masters last month and followed it up with another crown in Barcelona.
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However, the 14-time Grand Slam champion has a hard route to that potential matchup as he faces Fabio Fognini later Wednesday and potentially Nick Kyrgios in the third round.
Nadal had no such troubles as he dominated Kyrgios to beat the Australian in just over an hour.
David Goffin awaits the victor of Nadal's clash with Kyrgios as the Belgian beat world number six Milos Raonic 6-4, 6-2.
Raonic will face Belgium's David Goffin next.
However, after a bright start from the 20-year-old, tiredness kicked in as Cuevas, backed by a fervent support including Atletico Madrid duo Diego Godin and Antoine Griezmann, roared back to win the second set 6-0.
On the women's side, third-seeded Simona Halep of Romania reached the semifinals by beating Coco Vandeweghe of the USA 6-1, 6-1 in less than an hour.
The Spaniard won 7-6, 3-6, 6-4 and will now meet Australia's Nick Kyrgios, who overcame Ryan Harrison of the United States 6-3, 6-3.
Kuznetsova will face the victor of an intriguing clash between top seed Angelique Kerber and Eugenie Bouchard, who dumped out Maria Sharapova in thrilling fashion Monday.
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