The US Open champion fired home nine aces in a near two-hour encounter with the Bulgarian, while world number one Serena Williams also struggled in her match with Dominika Cibulkova.
Andy Murray overcomes Grigor Dimitrov to reach Miami Masters fourth round
Andy Murray fired home nine aces en route to a 7-6 (7/3), 6-3 victory over Bulgarian Grigor Dimitrov to battle into the fourth round of the Miami Masters last night.
The second seed, who won this event four years ago, needed one hour and 54 minutes to oust the 29th-seeded Dimitrov.
Murray said he got off to a slow start but soon figured out how to cause problems for his opponent.
"I was leaving the ball a bit short," said Murray afterwards.
"Once I started to improve my depth a bit I made it tough for him and he started to make mother mistakes after that."
Dimitrov, last year's runner-up to Novak Djokovic, would have faced a tougher task had not the 21-year-old lost his composure when serving for the first set at 5-3.
Dimitrov double-faulted three times to allow Murray to break back and the Scot duly prevailed in the tie-break.
It is the second time in as many tournaments that Dimitrov has cracked when serving for a set against a top-ranked player, serving up four double faults when he led world number one Djokovic 5-3 in the third round at Indian Wells.
"He probably got a little bit nervous, and that helped me," Murray said.
Murray, who committed 22 unforced errors to Dimitrov's 38, will face Italian Andrea Seppi in the fourth round, the 16th seed having beaten experienced Brazilian Thomaz Bellucci 7-5, 4-6, 6-2.
Meanwhile, eighth-seeded Frenchman Richard Gasquet rolled over 28th-seeded Russian Mikhail Youzhny 6-3, 6-4 and 10th-seeded Spaniard Nicolas Almagro beat Belgian David Goffin 6-3, 6-4. Gasquet faces Almagro in the fourth round.
Jo-Wilfried Tsonga, the number six seed, cruised past Jarkko Nieminen 6-3, 6-3, while Milos Raonic withdrew from the tournament with strep throat just moments before his match against Sam Querrey.
In the women's draw, Li Na set up a quarter-final against world number one Serena Williams despite an error-strewn performance as she ran out 7-6 (8/6), 6-2 win over giantkilling Garbine Muguruza.
The 31-year-old is playing in her first tournament since suffering an ankle injury in January's Australian Open final.
The 2011 French Open champion and two-time Australian Open finalist - made 39 unforced errors, including four double faults, and allowed her 19-year-old opponent to battle back to 5-5 in the first set having led 5-1.
Even at 6-1 in the tiebreaker Li faltered as 73rd-ranked Muguruza, who had claimed the scalps of the seeded Caroline Wozniacki and Anastasia Pavlyuchenkova in previous rounds, fought back to 6-6.
However, fifth-seeded Li pulled herself together to take the next two points and the set, before wrapping up victory in the second set.
Serena Williams also struggled having to come from a set down to win 2-6, 6-4, 6-2 against Slovakia's 13th seed Dominika Cibulkova.
Williams, who is bidding for a record sixth Miami title, admitted she had not been at her best and was 4-1 down to Cibulkova in the second set.
"I was struggling mentally, I was making so many errors," said Williams, who regained the number one spot in Doha in February but has not played since.
"I could not pull myself together. Someone (a fan) kept telling me to relax and I listened to him."
Elsewgere defending champion Agnieszka Radwanska defeated American Sloane Stephens 4-6, 6-2, 6-0 to reach the quarter-finals.
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