Fifth-seeded David Ferrer also breezed into the third round, beating Ivo Minar 6-3, 6-3.
Andreas Seppi upset eighth-seeded Richard Gasquet 6-3, 6-2. Gasquet is a having a woeful year - he's the only player among the top 42 not to have reached at least one quarterfinal match in 2008.
Davydenko dominated Ljubicic after the two players traded five breaks of serve early in the match.
"The first match is always difficult,'' said Davydenko, who had a first-round bye.
The Russian, who is coming off a third-round loss to Tommy Robredo in Rome, won the Masters tournament in Miami last month.
"Losing to Robredo was difficult, but the win in Miami has made me mentally stronger,'' Davydenko said.
The 29th-ranked Ljubicic, who reached as high as No. 3, has not beaten Davydenko in four years.
Luis Horna dropped out with a calf injury while trailing Potito Starace 6-3, 4-2 and Kristof Vliegen pulled out with a back injury with Jose Acasuso leading 5-2. Both were first-round matches. Filippo Volandri retired Monday with a knee injury.
Withdrawals have become a common theme in European clay-court tournaments in the past month.
The Rome Masters last week had five withdrawals and neither of the semifinals was completed.
The second-ranked Rafael Nadal, who lost in Rome in the second round after getting treated for a major blister on his foot, has blamed the crowded schedule for the series of retirements.
Robredo, the 2006 champion who lost in the first round last year, outlasted Philipp Kohlschreiber 2-6, 7-6 (5), 6-3.
Robredo, seeded 13th, was helped by a disputed call in the second set. Losing the point would have put Robredo down a break, but chair umpire Gerry Armstrong overruled the linesman, calling the ball good. A long discussion involving both players, Armstrong and the tournament supervisor followed. The point was eventually replayed and Robredo held serve.
"You try to shut it out but you keep thinking about it,'' Kohlschreiber said. "But it wasn't what decided the match. I made some bad decisions in my shots.
"Still, it's a pity. I think the umpire made a quick decision without checking the mark. He ruined what I had built up.''
Robredo broke serve for a decisive 4-2 lead in the third set. He double-faulted on one match point, but closed it out on the next one.
Stanislas Wawrinka, who lost the Rome final to Novak Djokovic, beat Alberto Martin 6-3, 6-3 to ease into the second round.
In another second-round match, Fernando Verdasco defeated Michael Llodra 6-2, 6-0.
In first-round action, 11th-seeded Carlos Moya rallied to beat Julien Benneteau 3-6, 6-4, 7-6 (7) and Janko Tipsarevic also came from behind to defeat Andreas Beck 3-6, 6-3, 6-1.
Nadal through to Barcelona Open quarters
Tsonga beats Mahut to advance at Hamburg Masters
