After narrowly surviving a 17-minute opening game, Murray made light work of a tricky opponent in
Djokovic endured a tough first set against
Murray was forced to save three break points in the epic opening game but came through it before going on to earn his own break of serve in the fourth.
The one break was enough to see the Scot seal the first set, the world number four serving out to love with a second serve ace down the centre of the court.
The second set was a similar affair, although this time it took Murray until the seventh game to break.
The Briton looked comfortable and more importantly confident as he quietly went about his game, eventually taking the lead before backing up his break to love with a hold to love.
And two games later, Murray booked his place in the last eight by serving out to love, again winning the game with an ace.
Next up for Murray will be Serbia's
Despite a tight opening set, ninth-seeded Tipsarevic ran away with the clash and easily wrapped things up when Dimitrov hit long.
Australian Open champion
Although Djokovic broke back in the sixth game, he remained far from comfortable as 17th-seeded Gasquet continued to cause him all sorts of trouble with forays into the net as well as some solid groundstrokes.
The Serb faced break points once again in the ninth game, only just denying the Frenchman on three occasions before going on to hold.
Three games later though and Djokovic had the set, Gasquet blinking at the crucial stage hitting consecutive groundstrokes long to give the Serb first blood.
The second set was a much more straight forward affair, Djokovic breaking in the fourth and sixth games before sealing the match in the ninth with a forehand winner down the line.
Next up for Djokovic is
The Spanish fifth seed dismantled his Argentine opponent in a hugely impressive 6-3 6-3 victory in the final match to finish under the floodlights on Stadium court.
But the Spaniard weathered the storm and broke back in the 10th game of the set, to reach the last four for the seventh time.
"The beginning was very tough for me. I think I started playing more aggressively, I started playing shorter and so I suffered a lot with my serves the beginning of the match," said Nadal.
"But later, at the end of the first set, I felt that I was starting to win my serves more easily than him. So the last couple of games of the end of the first set, I believe that I had more the control of the game."
Next up for Nadal will be a clash against sixth-seeded
A set and 4-2 up, Fish looked firmly in control against a lacklustre Almagro, only for the Spaniard to suddenly find his range and break back before racing through the tie-break for the loss of just two points.
And early in the final set Almagro even looked the more likely winner of the two, holding break points over Fish in the first, third and fifth games.
But the American stubbornly clung on, finally rediscovering his service rhythm in the seventh game to post back-to-back love service holds, with a break sandwiched between them, to seal the match.
Fish was denied the chance of an all-American quarter-final, however, when
Roddick, seeded 31 in Miami, looked a shadow of the player who beat Roger Federer 24 hours previously and produced a lacklustre performance that his Argentine opponent took full advantage of.