The fourth-seeded Russian took 1 hour 24 minutes to prevail over Croatia’s Ljubicic, a former top-three player who now ranks 29th.
Davydenko won the first two matches with Ljubic in 2003 and 2004, but lost the next three in the past four years. The series now stands at 3-3.
“The first match is always difficult,” said Davydenko.
The Russian faced stiff resistance in the first set which saw five breaks of serve. Davydenko then controlled the action in the second, winning on a forehand Ljubic hit wide. Davydenko had 13 unforced errors to Ljubicic’s 31.
Davydenko said his confidence was rattled when he lost to Spain’s Tommy Robredo in the third round in Rome last week, but he is overall more stable than in the past — boosted by his Miami Masters title in April.
“My tennis is still the same, but I am better mentally,” he said.
Fernando Verdasco of Spain also reached the third round, 6-2, 6-0 against Michael Llodra of France. There was more joy for Spain over France when Carlos Moya fought from 5-3 down in the final set to beat Michael Llodra, 3-6, 6-4, 7-6 (9-7), in the first round.
Two more players retired during first round games for a tournament total of three.
Belgium’s Cristoph Vliegen quit against Jose Acasuso with a back problem and Luis Horna of Peru likely damaged his calf muscle against Potito Starace of Italy. Filippo Volandri of Italy retired Monday with a knee injury.
Retirements have plagued tournaments in recent weeks, with world number three Novak Djokovic for instance not having to complete his quarter- and semi-final en route to the Rome title.
“What happened in Rome did not happen for no reason. One reason is the tight schedule. We need to talk about that more in the future,” said the Serb on Monday after arriving in Hamburg.
Djokovic, who is the hottest player in 2008, has a first-round bye like the world-leading duo of Swiss Roger Federer (a four-time Hamburg champion) and Spain’s Rafael Nadal. They start play in Hamburg on Wednesday.