World number one Djokovic won 24 of the last 27 points to reach a quarter-final against Spanish sixth seed David Ferrer, a 7-6 (7/5), 6-0 winner over Frenchman Gilles Simon at the ATP and WTA hardcourt tournament.
Ukraine challenger Dolgopolov was unable to stretch his lead to a double break in the second set, Djokovic saving two break points in the fourth game.
"I was really frustrated," Djokovic said. "I was trying to calm myself down, because inside there was a big fire. You could see a little bit of that in the first set.
"Just try to get to the state of mind where I have a serene, controlled mind and emotions and where I'm able to just be in the present moment. That's where I was focusing on."
The Serbian top seed turned the match on its head in a 22-minute final set in which he could do no wrong, sustaining his chance for a US double after his Indian Wells final victory over Roger Federer.
Dolgopolov began breaking down in the third set after getting blisters on both feet taped. Near the end he was clasping at his thighs with cramps as he went down to defeat.
"It wasn't my kind of a day," Djokovic said. "Just on the warmup the entire day was one of those days where you don't feel so great mentally.
"But I fought my way through. I was just trying to find a way to come back in the match. He was playing well. He has a very unorthodox game, tricky opponent, mixes up the pace, and can easily get you out of the rhythm."
Britain's Andy Murray won his 500th career victory, defeating South Africa's Kevin Anderson 6-4, 3-6, 6-3.
The third-seeded Scotsman, who holds two Grand Slam titles, needed his best effort against his 17th-ranked rival.
Murray, who has won four of five matches against Anderson, improved his career match record to 500 triumphs and 155 defeats with 31 titles, including the 2012 US Open and 2013 Wimbledon crowns.
"I hope I've still got a lot more wins in me," Murray said. "To get to 500 is good. It's not an easy thing to do at my age. It's nice. Hopefully I can keep going."
Murray is the first British man, the ninth active player and the 46th man in the post-1968 Open Era to achieve the 500-win plateau.
"There have not been loads of players that have done it. It's nice for me the fact that it happened here as well," said Murray, who trains in Miami in the off-season. "It's just fitting just because I have spent so much time training here and working to get better and to improve. That was nice."
Next up for Murray will be Austrian Dominic Thiem, who defeated Frenchman Adrian Mannarino 7-6 (7/5), 4-6, 7-5.
"He had his best year on the tour last year. He's a very talented guy. He's strong," said Murray. "I know him fairly well and practice with him quite a bit. I expect tomorrow will be a tough match."
Japan's fourth seed Kei Nishikori beat Belgian David Goffin 6-1, 6-2 with Nishikori set to move to a career-best fourth in the world, sending Rafael Nadal to fifth.
"I feel a lot of confidence. It's really going well these three matches," Nishikori said. "It's tough to compare, but maybe I have been playing a little better than last year."
Next up for Nishikori will be American John Isner, who won a big-serve duel with Canada's fifth-seeded Milos Raonic over two and three quarter hours. Isner's 6-7 (3/7), 7-6 (8/6), 7-6 (7/5) triumph featured a combined 35 aces but no service breaks.
Another quarter-final was set as Czech eighth seed Tomas Berdych advanced thanks to a mid-match withdrawal from France's injury-hit Gael Monfils.
Berdych won 6-3, 3-2 when his opponent stopped a game after falling heavily on his right hip. Monfils has now withdrawn 15 times in his career.
Berdych will play Argentina's Juan Monaco, a 6-3, 6-3 winner over Fernando Verdasco. Monaco will be playing in the last eight at the ATP Masters level for the first time in three years.
On the women's side, Spanish 12th seed Carla Suarez Navarro eliminated three-time Miami winner Venus Williams 0-6, 6-1, 7-5.
The Spaniard advanced to a semi-final against German ninth seed Andrea Petkovic, who ousted Czech 14th seed Karolina Pliskova 6-4, 6-2.
Britain's Murray takes milestone 500th victory
Britain's Andy Murray won his 500th career victory Tuesday, defeating South Africa's Kevin Anderson 6-4, 3-6, 6-3 to reach the ATP and WTA Miami Open quarter-finals.
The third-seeded Scotsman, who holds two Grand Slam titles, needed his best effort against his 17th-ranked rival.
Murray, who has won four of five matches against Anderson, improved his career match record to 500 triumphs and 155 defeats with 31 titles, including the 2012 US Open and 2013 Wimbledon crowns.
A brief post-match ceremony paid tribute to Murray's achievement.
Murray is the first British man, the ninth active player and the 46th man in the post-1968 Open Era to achieve the 500-win plateau.
Next up for Murray will be Austrian Dominic Thiem, who defeated Frenchman Adrian Mannarino 7-6 (7/5), 4-6, 7-5.
Also advancing was Japanese fourth seed Kei Nishikori, who dispatched Belgium's David Goffin 6-1, 6-2. That will push Nishikori to fourth in the world rankings with Spain's Rafael Nadal falling to fifth.
Nishikori next will face the winner of a later match between Canada's Milos Raonic and American John Isner.
Another quarter-final was set as Czech eighth seed Tomas Berdych advanced thanks to a mid-match withdrawal from France's injury-hit Gael Monfils. Berdych won 6-3, 3-2 when his opponent stopped a game after falling heavily on his right hip. Monfils has now withdrawn 15 times in his career.
"In the end I feel sorry for Gael. That's not the ideal way to finish up the match," Berdych said. "But in the end, I'm through. That's what matters. That's what counts.
"I'm happy with the win. Really it's not the way that you want to finish the match, but that's how it is. So we need to move on and just go for the next one."
Berdych will take on Argentina's Juan Monaco, a 6-3, 6-3 winner over Fernando Verdasco. Monaco will be playing in the last eight at the ATP Masters level for the first time in three years.
Spanish sixth seed David Ferrer beat French 12th seed Gilles Simon 7-6 (7-5), 6-0.
On the women's side, German ninth seed Andrea Petkovic ousted Czech 14th seed Karolina Pliskova 6-4, 6-2.
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