Ana Ivanovic earned a spot in the women's semifinals with a 6-3, 6-4 victory over Marion Bartoli, the 16th-ranked Serb's second straight win over a top-10 player.
She will play Maria Sharapova, who needed more than three hours to subdue fellow Russian Maria Kirilenko 3-6, 7-5, 6-2. Kirilenko had won eight of nine three-setters this year, but six double faults, including on match point, and weak second serves did her in.
American John Isner defeated Gilles Simon of France 6-3, 1-6, 7-5, setting up a semifinal against Djokovic.
"This is my first match on this court this year and I had to adjust," said Isner, who played his other matches on outer courts. "I didn't get too frustrated. I made a lot of mistakes, but he does that to a lot of players."
Sharapova broke Kirilenko three times in the final set, when Kirilenko's father-coach came on court with her trailing 4-0. The chair umpire turned him away because she didn't first ask permission. Kirilenko also was penalized a point for hindrance in the second set after she tapped her racket on the court three times during a point.
"It's one thing if you do it once, but I think she did it three or four times," Sharapova said. "It's not like a hockey puck or something. She forgot, I think, the sport."
Sharapova and Kirilenko needed 2 1-2 hours to split sets, with Kirilenko calling for a trainer early in the second set to have her ankle taped.
"I really felt like I could improve on so many things during the match and change things around," Sharapova said. "Little by little, I started doing those things better."
Sharapova fought off five break points to hold at 3-2 in the second set during a roll in which she won five straight games to lead 4-3. The women traded service games before Sharapova held at love to go up 6-5 and then she broke to close out the second set, 7-5, on Kirilenko's netted forehand.
"Little by little I started feeling better. Towards the end I really got my groove back," Sharapova said.
Defending champion Djokovic improved to 16-1 against Spanish opponents since the start of 2011, although Almagro made him work for it on another 80-degree day at the Indian Wells Tennis Garden. Almagro held with a backhand winner down the line to go up 4-3 in the second set.
Djokovic served at 40-love in the next game before Almagro rallied to reach deuce. Djokovic held, then broke Almagro in the next game and served out the match with a 40-love game that ended with his own backhand down the line.
"I didn't lose many points on my service games in both sets, and that's something that I have been working on. I have been trying to get more free points on the first serves," he said. "This obviously hasn't been my weapon in the past, so I tried to use my serve in the best possible way, and then it gives me more confidence for what's coming up after that."
Ivanovic had knocked off defending champion and fourth-ranked Caroline Wozniacki in straight sets in the fourth round. Ivanovic is trying to regain the form that made her No. 1 in 2008, when she won her only Grand Slam title at the French Open and won at Indian Wells.
Bartoli, runner-up here last year, requested a doctor for an on-court evaluation early in the second set. She said she began feeling sick on Wednesday night and suspected she has the same viral illness that derailed several players during the two-week tournament.
"Even though we didn't have very long rallies, I was feeling really out of breath," she said. "Then I was having a lot of joint pains and feeling shaky and very cold. It was quite hot, so I knew I was not in a good shape. Even though I lost it, I just felt like I needed to stay there until the end."
Bartoli broke Ivanovic to open the match, then Ivanovic took control and broke to open the second set before finishing it off in less than 1 1-2 hours.
Ivanovic moved into her first semifinal of the season, having reached the quarter-finals in Dubai and losing in the fourth round of the Australian Open. She won one title late last year at Bali. After her big year in 2008, Ivanovic dropped out of the top 20 in October 2009, falling as low as No. 65, before returning to the top 20 at the end of 2010.
"When you're young and upcoming you don't have these experiences. You don't know what to expect or what the consequences are," the 24-year-old Serb said. "Then with so many experiences and everything, it does help you at some points, but also it sometimes creates a doubt because you analyze and think too much. But I'm just very happy that the work I put in is paying off and I'm starting to put it together in matches, in the big matches, too."