Djokovic, the defending champion, knocked off Guillermo Garcia-Lopez 6-4, 6-4 while Murray won 6-2, 6-3 over Igor Kunitsyn. They are the two highest seeded players in the field after world No. 1 Roger Federer's withdrawal because of a lung infection.
Djokovic was in control much of the match, using an early break en route to the first-set win and leading 5-0 in the second before faltering slightly.
Garcia-Lopez broke Djokovic's serve twice before the Serb was able to finish off the match.
Murray was on the court 1 hour, 41 minutes -- surprisingly long for a match in which he dropped just five games. He had 13 aces but got just 52 percent of his first serves in.
The only other seeded player in action Monday was No. 8 Gilles Simon, who was ousted by Marcos Baghdatis 7-6 (7-3), 6-4.
Other first-round matches saw Jurgen Melzer top Simone Bolelli 6-1, 7-5; Stefan Koubek beat Feliciano Lopez 7-6 (7-4), 6-4; Ivan Ljubicic slip by Jan Hernych 6-2, 6-7 (3-7), 6-4; and Viktor Troicki defeat Rainer Schuettler 6-3, 6-4.
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