Jankovic will end the year as world number one regardless of Doha results
Serbia's Jelena Jankovic comfortably beat compatriot Ana Ivanovic 6-3 6-4 in their opening match of the round-robin Tour Championships in Doha.
In blustery conditions, Jankovic took just 40 minutes to win the first set while she looked at ease in the second even though Ivanovic improved slightly.
Venus Williams overturned a 5-2 deficit in the first set to power to a 7-5 6-3 win over Russia's Dinara Safina.
Earlier, Vera Zvonareva beat Svetlana Kuznetsova 6-2 6-3 in the White Group.
Zvonareva admitted she found it difficult to adapt to playing outdoors, saying: "The conditions are very difficult, especially since we were playing indoors for the past two months."
Two players from each group will advance to the semi-finals of the season-ending tournament, with Ivanovic now facing an uphill task.
Ivanovic had won her last six matches with Jankovic, the most recent of which was the semi-final victory at this year's French Open.
But the 20-year-old has struggled for form in the latter half of the year, with last week's victory in the Linz Open her first tournament win in four months, and on this form she will be happy to see the season end.
The world number four never looked like continuing her impressive record over Jankovic as, even though she hit some spectacular winners, she made a number of errors.
Jankovic, on the other hand, who will remain top in the rankings regardless of results in Doha, is in prime condition to win the tournament.
She raced to a 3-0 lead in the first set and although Ivanovic, last year's semi-finalist, hinted at a comeback when she went on to win two on the trot, Jankovic broke serve again and cantered to a 1-0 set lead.
There were some tough games there, but they kept going my way
The second set mirrored the first as Jankovic broke early. In the sixth game of the set, Ivanovic proceeded to win five points in a row to level the score at 3-3, but from then on Jankovic took control of the match.
Williams trailed 5-2 in the first set of her encounter with Safina, before turning the match on its head with five successive games.
The dramatic change in the complexion of the match dented Safina's confidence, and Wimbledon champion Williams had far less trouble in the second set.
"I was able to make the adjustment," Williams said of her first-set recovery. "There were some tough games there, but they kept going my way."