The poor weather in Madrid led to the roof at the Manolo Santana court being closed which took some of the effectiveness off Lopez's powerful serve, giving Djokovic an advantage in a tournament held at altitude where the ball is considered to fly faster than at other events.
"I think that even though I played really badly, my attitude has been very positive", Nadal explained. "I'm expecting the best Djokovic tomorrow".
Nadal finally broke in the third game of the second set before having to stave off four break points on his own serve to consolidate his lead at 3-1.
And only poor returning on his break point opportunities denied Nadal just as convincing a scoreline as the Spaniard took only two of his 14 chances.
Djokovic, the World No. 2, is in the middle of his worst season since 2010.More news: EVM controversy: Just a technical issue or big conspiracy
Djokovic rallied in the final set by breaking Almagro to go up 6-5 and served out to earn his 15th win of the season in over two hours.
Curling a running forehand victor, Lopez issued a love hold for 3-all.
Unseeded Sevastova was playing her first semifinal at premier mandatory level, the grade immediately below grand slam tournaments. "I started the match OK, but when I started to go behind, I didn't find any way to improve my game or to make it more hard for him", Murray told a news conference.
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.
Fifth seed Milos Raonic is also into the last 16 as he got the better of a battle between two big servers, winning 6-4, 6-4 against Gilles Muller. Raonic will play Belgium's David Goffin next.More news: Voters split on whether Comey firing was right
Kei Nishikori of Japan talks to the media after withdraw from the Madrid Open with an injury before his quarterfinal against Novak Djokovic. Tomas Berdych, the 11 seed, also progressed into the third round following a 7-6 (5), 6-3 win against Robin Haase of the Netherlands.
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.
Djokovic, who has refused to rule out appointing Andre Agassi as coach, prowled around the court and had the bit between his teeth as he stayed in the hunt for only a second title of the year with the French Open on the horizon.
"I'm going to think about who I want in my team and I don't yet have anyone".
"I played aggressively and used a lot of forehands".More news: China to import poultry, beef in new USA trade deal
"There are not too many of those kind of champions in the history of the sport. I can't talk more than that".
- Portugal win first ever Eurovision Song Contest
- Trump promises to protect Christians at Liberty commencement speech
- US, EU in urgent talks on expanding laptop ban on flights
- NHS braced for possible repeat of cyber attack chaos on Monday
- Pga: Kim youngest winner of Players Championship
- North Korea: New long-range missile can carry heavy nuke
- Alonso's Indy 500 car will go to his museum
- What time is it? Who has qualified? Who can England face?
- Australia receptive to China's Silk Road, but national interest first
- Know All About How Mother's Day Was Founded