Federer, who lost to the fifth-ranked Swede in the exhibition tournament last year, struggled with his serve in the first set and had to save several break points early on. He then made several unforced errors in the tiebreaker, handing Soderling the lead when he hit a forehand long on set point.
But the No 2-ranked Swiss took control in the second set, breaking Soderling twice with the help of his powerful forehand. Trailing 5-3, Soderling double faulted to give Federer a set point and the Swede then sent a shot that bounced on the net cord and out to even the match.
In the third set, Federer broke for a 5-3 lead when Soderling missed an easy forehand, before closing out the match with an ace.
"It's always good to win," said Federer, who lost his first match in both previous editions of the tournament. "I thought I played a good match. I never got broken today. I came back and got through a tough second set and third set I felt I was playing better."
Soderling said he wasn't able to "get into my rhythm at all."
"It was a tough match, like always against Roger," Soderling said. "He played really fast. But overall it was a pretty good match. Maybe I did not serve well in the last two sets."
Nadal struggled against the sixth-ranked Berdych's serve at the start before breaking for a 5-4 lead with a forehand into the corner. He clinched the set with another forehand winner.
Nadal, the defending champion, jumped out to a 4-1 lead in the second, breaking Berdych twice before the 25-year-old Czech took the next two games to make it 4-3. But Berdych's comeback fell short and Nadal closed out the match with a forehand that the Czech returned into the net.
"It was a very good match as the first of the year and against a very good opponent like Tomas," Nadal said. "Abu Dhabi is the perfect place to start the season."