To secure his spot against Roddick, Ljubicic won against 23-year-old David Nadal, the defending champion who was playing his first tournament since a knee injury forced him out of the Australian Open.
Roddick and Söderling both fought frustration as momentum shifted in their battle.
Roddick broke his racquet on the ground after dropping his serve in the eighth game of the second set, leaving Söderling to serve for the set at 5-3.
The Swede made the most of it with a love game, then the two traded breaks early in the third before Roddick earned the decisive break for a 4-2 lead that he never relinquished.
Roddick said he was conscious of Söderling’s pressure on his serve, but he was able to apply the same to the Swede.
“I knew I was returning real well, so I thought this might be the rare occasion where that would be the thing that won it for me,” Roddick said.
Even after he won the second set, Söderling said he didn’t feel he was playing great.
“He played a little bit better than me,” Söderling said. “I think he served a little bit better, and then I made a few more unforced errors. That’s about it.”