Murray, who won the tournament in 2009 and 2011, stopped Nicolas Mahut 6-3, 7-6 (7-4) in a second-round match and turned around for a 6-2, 6-2 romp over Marinko Matosevic in 56 minutes in the third round.
Murray lost his serve once in the four sets and ended up with seven breaks, five coming against Matosevic.
No. 4-seeded Jo-Wilfried Tsonga also won twice Thursday, getting past Edouard Roger-Vasselin 6-3, 6-7 (2-7), 6-3 before beating Igor Sijsling 7-5, 5-7, 7-3. Each match took about 1 hour, 45 minutes.
All but two of the top eight seeds advanced to the quarterfinals. Benjamin Becker took one of the other two berths with a tight 7-6 (7-5), 7-5 decision over seventh-seeded Alexandr Dolgopolov and Denis Kudla beat Kenny de Schepper 6-1, 6-3 to claim the other.
The quarterfinals Friday call for Murray to play Becker while Tsongas meets Kudla. Also, Berdych goes against Cilic and del Potro draws Querrey.
Swim Week Miami Beach 2014 [PHOTOS]