The fifth-ranked Murray, who dropped below No. 4 Soderling in last week's rankings, kept the ball away from the Swede's strong forehand on the indoor court at the O2 Arena.
Soderling, who again reached the French Open final this year and won the Paris Masters for the first time, had only five forehand winners while committing 12 unforced errors with his often dominating shot.
Murray looked to be the more solid player throughout, facing only one break point in the match while converting three of his six.
The Briton earned his first break early in the match, hitting a backhand winner off Soderling's serve to make it 2-1. He converted another to make it 5-2 and then served out the first set with a drop shot that hit the line.
In the second set, Murray broke again after taking a 0-40 lead in the seventh game.
Murray and Soderling are in Group B at the round-robin tournament. Roger Federer and David Ferrer, who play later Sunday, are also in the group.
Group A will take the court on Monday with top-ranked Rafael Nadal facing Andy Roddick and Novak Djokovic playing Tomas Berdych.
In doubles, top-ranked Bob and Mike Bryan of the United States defeated Jurgen Melzer of Austria and Philipp Petzschner of Germany 6-3, 7-5.
