Top-seeded Djokovic had to fight back from a break down in the last set to beat Jan Hernych of Czech Republic 6-3, 3-6, 6-4 over more than two hours, while second-seeded Murray cruised past Arnaud Clement of France 6-2, 6-3.
"I think Hernych played really well,'' Djokovic said. "He had nothing to lose and was going for winners, while I became a bit defensive.''
Djokovic, yet to reach a final this year, will next play fifth-seeded Marin Cilic, who already has two titles this season in Chennai and Zagreb.
Cilic overcame Julien Benneteau of France 6-3, 4-6, 7-5 in his second straight three-setter.
"I was quite relieved when I won this one,'' Cilic said. "He was playing very well on those big points, and he was serving very, very good. It was tough for me to be in position to get a break, especially in the second set.''
Murray was another double winner on the tour, with titles from Doha and Rotterdam.
Clement had won both of their previous encounters in 2006 when Murray was 18, but the Scot was now ranked No. 4 in the world.
"The last couple of times we played, I was very young and he was a very experienced player,'' Murray said. "But I am happy that I played much better than my first round. I served a whole lot better and didn't give him any chance to break. I think I adjusted well tonight.''
Murray said he still felt soreness in his ankle, which he injured during his win at Rotterdam.
"It changes where it hurts from day to day. Sometimes it's on the serve, and sometimes it's when I am hitting a forehand. Sometimes it hurts more when I'm walking rather than running,'' he said. "I just have to sort of see what it's like when I wake up, and deal with it.''
Next up for Murray will be unseeded Richard Gasquet of France, who took more than three hours to edge Simone Bolelli of Italy 6-7 (4), 6-3, 7-6 (5).
Third-seeded Gilles Simon of France dispatched Teimuraz Gabashvili of Russia 6-1, 6-2, conceded only 11 points on serve, and set up a quarterfinal with countryman Fabrice Santoro, who beat qualifier Marco Chiudinelli of Switzerland 3-6, 6-1, 7-6 (1).
The 36-year-old reached the inaugural Dubai final in 1993, and won it in 2002.
The other quarterfinal pits fourth-seeded David Ferrer against sixth-seeded Igor Andreev.
Spain's Ferrer beat Germany's Philipp Kohlschreiber 6-4, 6-2, and Andreev topped fellow Russian Dmitry Tursunov 5-7, 6-4, 6-3.
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