American Andy Roddick also won, reaching the second round with a 6-0, 7-6 win over Argentina's Jose Acasuso.
Sixth-seeded Tommy Haas saw his outside chance of qualifying for the Masters Cup fade when he was beaten 6-3, 4-6, 6-0 by Dominik Hrbaty, and seventh-seeded Spaniard Juan Carlos Ferrero was defeated 5-7, 7-6, 6-3 by Austria's Jurgen Melzer.
Top-seeded Ljubicic fired 15 aces against Mayer, four in succession in one game, and that gave him the edge over an opponent who rallied well but had no real weapon to trouble the Croatian.
Ljubicic set the pattern by holding the opening game with successive aces, and broke to lead 3-1 when Mayer netted a forehand. Ljubicic had just one anxious moment, holding off a break point in the next game by hitting a winner after reaching a dropshot.
Ljubicic maintained the pressure in the second set, but needed patience before breaking to lead 3-2 with a crosscourt forehand. A further break with a winning return gave him the match.
"For me it was a very, very good match. I'm very satisfied," Ljubicic told reporters. "I had the match under control pretty much the whole time. When I serve like this, when I feel the ball perfectly, a lot of things are easy and if I play the way I play today it's going to be very difficult to beat me."
Roddick found even more firepower in overcoming Acasuso, hitting 19 aces.
The U.S. Open runner-up completely overwhelmed Acasuso in the first set, holding the first game to love and breaking for 2-0. When Acasuso won the first two points on Roddick's next serve, he responded with four straight aces to hold.
After dropping just three points on serve in the first set, Roddick was finally stretched in the second as his opponent found the range with his own serve and hit nine aces.
Roddick held a break point at 3-2 but Acasuso forced a backhand error, and the American also failed to win three match points at 6-5 before sweeping the tiebreak for the loss of just two points.
"It felt good, especially the first set," said Roddick. "I felt like I was hitting the ball pretty clean the whole match. In the second set I felt he started making a lot more first serves, but I got through the tiebreak comfortably and felt in control the whole match."
Roddick will face Richard Gasquet in the second round after the Frenchman beat Alejandro Falla of Colombia 7-6 6-3. The American will treat him with respect.
"I don't think you could have hand-picked a tougher second round draw in this tournament," said Roddick. "He's a very, very good player and he did well in the summer, and I have a lot of respect for Richard's game."
