Murray defeated Russia's Igor Kunitsyn 6-2, 6-3 at the $1.6 million tournament, while the second-seeded Djokovic beat Guillermo Garcia-Lopez of Spain 6-4, 6-4.
Murray got off to a nervous start and Kunitsyn kept it close in the first set, rallying from a 3-0 hole by holding serve and breaking Murray to make it 3-2. But the 22-year-old Briton won the next three games and took the set with a superb forehand.
Story continues below ↓advertisement | your ad hereKunitsyn started the second set well, breaking Murray in the first game, but the world's fourth-ranked player broke back immediately and then held his serve to go ahead 2-1. He broke Kunitsyn a second time in the sixth game and thwarted his attempts to recover.
Djokovic had just as little trouble with Garcia-Lopez, breaking him to go 2-0 up and eventually holding on until he double-faulted for set point.
The 22-year-old Serb quickly took a 5-0 lead in the second set before Garcia-Lopez fought back, breaking Djokovic twice in the seventh and ninth games to make it 5-4. But Garcia-Lopez failed to hold on to his serve when it mattered most, allowing Djokovic to take the second set 6-4 and with it the match.
"It was not pleasant coming from 5-Love to 5-4 and him serving to get back into the match, but it was all my fault. I think I lost focus," Djokovic said. "It's the first match outdoors since Australia, so still getting used to the conditions.
Djokovic is trying to defend a tournament title for the first time. He'll play fellow Serb Victor Troicki on Wednesday, after his 6-3, 6-4 win over Rainer Schuettler.
"It's a success that I am still trying to achieve, to defend my title," Djokovic said. "I haven't done it in my career so I am really hoping that it's going to be this week."
Djokovic, Andy Murray, Nikolay Davydenko, Jo-Wilfred Tsonga and Marin Cilic are the only top 10 players in the field after No. 1-ranked Roger Federer pulled out of the tournament on Sunday due to a lung infection.
Also Monday, Marcos Baghdatis of Cyprus knocked out eighth-seeded Gilles Simon 7-6 (3), 6-4, while Ivan Ljubicic of Croatia defeated Jan Hernych of the Czech Republic 6-2, 6-7 (3), 6-4.
Austrians Jurgen Melzer and Stefan Koubek advanced after both won in straight sets. Melzer beat Simone Bolelli of Italy 6-1, 7-5, and Koubek defeated Feliciano Lopez of Spain 7-6, 6-4.
© 2010 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.Primera Liga round-upDjokovic, Youzhny advance; Llodra, Ljubicic lose