Playing his first round robin match at the elite tournament this year, Djokovic extended his winning streak to 18 matches after capturing his sixth title of the season last week in Paris, where he defeated Federer in the semifinals.
Djokovic is trying to finish No. 1 for the third year in a row but Nadal, who eased past David Ferrer 6-3 6-2 yesterday, needs only one more win in London to be guaranteed the top spot.
Federer and Djokovic easily held their serve until the ninth game when the Serb found himself 15-30 down.
A double fault gave Federer his first break point but the former World No. 1 sent a forehand wide on the next point before Djokovic took the next two points to hold his serve.
The Serb earned two break points in the next game with a superb backhand return. The cheering from the legion of Swiss supporters packed in the stands did not help Federer as he fluffed a forehand to lose the set.