Defending women's champion Victoria Azarenka extended her own streak despite a nagging right ankle problem, routing Urszula Radwanska 6-3, 6-1 for her 17th straight win. Urszula's sister, third-seeded Agnieszka Radwanska, was beaten by No. 13 Maria Kirilenko, 6-1, 4-6, 7-5.
No. 3 Andy Murray beat Yen-hsun Lu of Taiwan 6-3, 6-2 in their first meeting in five years.
No. 8 Caroline Wozniacki defeated No. 10 Nadia Petrova 7-6 (3), 6-3 to set up a quarterfinal against Azarenka that matches former top-ranked players against each other.
Djokovic trailed 5-3 in the first set when the 21-year-old Bulgarian committed six double-faults, including four in one game, to help the Serb force the tiebreaker. Djokovic won it on a backhand error by the youngest player remaining in the draw.
"It was not really a beautiful match to watch," Djokovic said. "There were a lot of unforced errors, and we both look quite sluggish on the court."
Dimitrov was broken twice in the second set while falling to 1-17 against top-10 opponents.
"He did all the work making winners and making unforced errors," Djokovic said. "I just needed to hang in there and try to be patient."
Djokovic moves on to play Sam Querrey, a 7-6 (5), 6-7 (7), 7-5 winner over Marinko Matosevic.
Djokovic hasn't lost since Oct. 31, when Querrey beat him at the indoors Paris Masters.
"He does everything really well: unbelievable forehand, unbelievable backhand, moves around the court great, returns great. It's tough to pick on something," Querrey said. "I might have to go outside of my comfort zone a little bit and do things I don't like to do, and hopefully it will pay off for me."
Querrey is poised to take over as the top-ranked American in the men's game -- albeit not in the top 10 -- from Mardy Fish, who lost 7-6 (4), 7-6 (0) to No. 8 seed Jo-Wilfried Tsonga.
"The most important thing is your world ranking," Querrey said. "If you're top 10 I think you're seen a little differently."
Azarenka was clearly bothered by her right ankle, wincing after shots. She also has a stuffy nose.
"I could overcome those things and manage to take these chances in the important moments and really go for my shots, to make that happen, not to wait for her mistake," she said. "Because at some point I was waiting for her mistake, and I can't do that. She wasn't missing because she's a very, very consistent player, so I decided to just take everything in my own hands and see where it takes me."
No. 2 Maria Sharapova joined Azarenka in the quarterfinals with a 7-5, 6-0 win over Lara Arruabarrena-Vecino of Spain, someone she had never played before.
Sharapova trailed 2-0 and 3-2 in the first set before rallying on a cloudless day in the desert when temperature reached the lower 90s.
"Just didn't get a good rhythm on her game from the beginning," she said. "Maybe I was going for the lines a little bit more than I had to, especially in the first few games when you don't know too much about your opponent or haven't played her.
"Towards the end of the first and beginning of the second set I really stepped it up, was being more aggressive, and really gave myself a better margin than I did throughout the first set."
Tsonga has beaten Fish all four times they have played. The Frenchman next plays 17th-seeded Milos Raonic, who outlasted Marin Cilic 3-6, 6-4, 6-3.
"I'm going to have to serve well and try to get ahead on his second-serve points," Raonic said about Tsonga. "When he's making his first serves he serves really well and it's tough."
Fish lost in the third round for the second straight year. He is playing his first tournament since last September after being sidelined with a heart condition, although he hasn't disclosed the exact nature of the problems.
"I certainly missed playing tennis for a living. I certainly missed making money, got bills to pay," he said. "It's a tough thing because the last time that I was on the tennis court was some of the worst times I have ever had. That part is very hard to deal with. It's not easy to come back from that. This week is a good step in the right direction."
Fish is still in contention in doubles with partner James Blake, and he plans to play in Key Biscayne, Fla., next week.
In other men's matches, No. 7 Juan Martin del Potro beat Bjorn Phau 6-2 7-5; 19th-seeded Tommy Haas got by No. 11 Nicolas Almagro 6-3, 6-7 (2), 7-6 (2), and Carlos Berlocq defeated No. 16 Kei Nishikori 6-2, 6-2.
On the women's side, No. 4 Angelique Kerber beat qualifier Garbine Muguruza 6-4, 7-5; fifth-seeded Petra Kvitova beat No. 19 seed Klara Zakopalova 6-2, 6-3; No. 7 Sam Stosur got by No. 24 Mona Barthel 4-6, 6-2, 6-3; and sixth-seeded Sara Errani defeated No. 9 Marion Bartoli 6-3, 6-2. Errani next faces Sharapova.