In other matches, Venus Williams beat second-ranked Dinara Safina 7-5, 6-3, and ninth-ranked Vera Zvonareva defeated Svetlana Kuznetsova 6-2, 6-3 in an all-Russian matchup.
Jankovic displayed the composure and consistency that have ensured she will end the year as the top-ranked player. Her Serbian compatriot alternated between spectacular winners and a far greater number of errors, drilling a backhand into the net on match point.
Ivanovic went into the match with a 6-1 record against Jankovic, with the last victory in three sets on her way to the French Open title in June. This time, Jankovic took charge early and showed she is a different player in terms of stroke production and mental strength.
"I've improved so much since the last time we played,'' said Jankovic, who has not won a major but established her late-season dominance with three consecutive titles at Beijing, Stuttgart and Moscow. "My game has gone to another level.''
Jankovic often smiles during play, but she showed little emotion in an efficient performance on a purple, outdoor hard court, a change for top players who are emerging from an indoor season. Gusts swirled around the stadium at the Khalifa International Tennis Complex, and Jankovic adjusted her shot selection while Ivanovic stuck to aggressive play that allowed little margin for error.
"It's the one who stays focused (who wins),'' Jankovic said. "You need to use a little bit more of the brain.''
Ivanovic paused late in the second set with dizziness caused by dehydration in humid conditions.
"I just felt so weak,'' said Ivanovic, who had a string of early-round losses linked to injury after her success at Roland Garros. She won a title last month at Linz, Austria, which restored some confidence. However, she was unable to repeat that form.
"The conditions here are completely different,'' Ivanovic said. "It's also a little bit slower, so it's very hard to make a winner.''
Williams trailed 5-2 in the first set, but turned the match around with five straight games. The startling shift in momentum shook Safina's confidence, and the Wimbledon champion had 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.''
Williams said she probably wouldn't turn on a television to watch coverage of the U.S. presidential elections.
"I'm not a super-political person,'' said Williams, a Jehovah's Witness who does not vote for religious reasons.
Like Jankovic, Zvonareva seemed more comfortable with the wind, as well as a noisy crowd, against Kuznetsova, who often yelled in frustration after mistakes.
"The conditions are very difficult, especially since we were playing indoors for the past two months,'' Zvonareva said.
On the second day of play Wednesday, Ivanovic faces Zvonareva, Venus Williams plays Elena Dementieva, and Safina is up against Serena Williams.
The top eight players in the world are divided into two round-robin groups. The top two in each group will advance to an elimination stage.
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