Djokovic took out Bernard Tomic 6-3, 6-3 in just more than an hour. Djokovic won the first four games of the match and ended up with four breaks. He dropped his serve once in the opening set after building the big lead but didn't see a break point in the second.
Murray was on the court more than 2 1/2 hours in getting past David Nalbandian 6-1, 4-6, 7-5. The only game Murray lost in the first set was on serve and Nalbandian dropped just five points on serve in taking the second set. But Murray managed a break in the 11th game of the third set and was able to advance.
Also in the second round, fifth-seeded Jo-Wilfried Tsonga defeated Viktor Troicki 6-3, 6-2 and No. 6-seeded David Ferrer edged past Fernando Verdasco 6-3, 7-6 (7-3) but Juan Carlos Ferrero ousted 13th-seeded Gael Monfils 7-5, 6-3.
Marcel Granollers upset No. 15-seeded Feliciano Lopez 6-4, 6-4 and 10th-seeded Juan Martin del Porto needed a third set to advance 7-5, 3-6, 6-4 over Michael Llorda.
Other seeded players winning first-round matches Tuesday were No. 11 Gilles Simon, 14th-seeded Juan Monaco and No. 16 Richard Gasquet. Lukasz Kubot and qualifiers Guillermo Garcia-Lopez and Sam Querrey also advanced to the second round Tuesday.