Davydenko was stretched by South Korean opponent Lee Hyung-taik before emerging a 7-5, 6-4 winner while Ljubicic, a two-time runner-up in Doha, scored an easy 6-1, 6-2 victory over qualifier Denis Gremelmayr of Germany.
Olivier Rochus caused the first upset of the tournament, defeating seventh-seeded Frenchman Sebastien Grosjean 6-4, 6-4.
Eighth seed Stanislas Wawrinka of Switzerland also fell, losing to Max Mirnyi of Belarus 5-7, 6-4, 6-4.
Davydenko was the overwhelming favourite against Lee but the South Korean had other plans. A silver medallist at last month's Asian Games in Doha, he troubled a rusty-looking Davydenko.
"It was a tough first match as the balls were slow. I had trained with faster balls in Mauritius before coming here and it was difficult to adjust," Davydenko told reporters.
"I have not thought about becoming world No. 1 as yet. I have just won my first match of the season. Maybe if I win the Australian Open, we can talk about that."
In sharp contrast to Davydenko, Ljubicic wrapped up the match in less than an hour, using his powerful serves and baseline play to overcome his opponent.
"It was a good win," he said. "I am happy with my performance especially as I have recovered from last season's illness."
Ljubicic had to pull out of the Paris Masters following a virus in November last year.
"I was worried that the illness would affect my career, but now I have fully recovered and I feel fully fit. Hopefully I can keep up this form throughout the season," he said.
Earlier, Moroccan wild card entry Younes El Aynaoui pulled off a stunning 7-6 (7-5), 7-6 (6-1) win over 2002 Australian Open champion Thomas Johansson of Sweden.
"This is a great win. It shows that I am ready for the circuit and that I have recovered completely from my injury," Aynaoui said.
In another first round match, Federico Luzzi of Italy beat Austria's Juergen Melzer 5-7, 6-4, 7-5.
