"I've always been a good player off the jump," Williams said. "That's kind of always been the way I've played throughout my career. I never played a lot of big warm-up events. Coming to tournaments, I've always been able to play well when I entered."
Team Americas went on to defeat Team Europe 2-1 when Argentina's Gisela Dulko beat Hungary's Agnes Szavay 6-4, 6-7 (8) 6-3. Team Americas will next play Team Russia.
Williams served and hit powerfully, while Jankovic appeared sluggish, with serves lacking pace and erratic groundstrokes.
Jankovic said she is usually a slow starter and adjusting to a bulkier body following an offseason fitness program.
"I need more time to adjust, to get my rhythm and feel the court, feel the ball," Jankovic said. "You could see, I was very, very slow out there. My reactions were quite slow."
Williams also beat Jankovic in the semifinals of the season-ending WTA Championships in Doha, Qatar, on her way to winning the title.
The American broke in the first and third games to go up 4-0 in the first set. Jankovic squandered four break points in the sixth game to fall 5-1 behind, and Williams served two aces and hit a down-the-line forehand winner to close out the set.
Jankovic dropped serve in the third game of the second set to trail 2-1. She missed a forehand in the seventh game to give Williams a second break and a 5-2 lead. Williams served an ace and two other serves forced errors in the next game to clinch victory.