Earlier, fifth-ranked Li Na edged Sara Errani 6-3, 7-6 (5). Errani also lost her opening group match on Tuesday to Azarenka and likely will be eliminated from the round-robin event featuring the top eight players in the world.
Jankovic, who was ranked No. 1 in 2008 and returned in the top 10 for the first time since 2011, outplayed the erratic Azeranka to snap a four-match losing streak against her.
Li trailed 3-1 in the second set but won the next four games -- and then couldn't close it out. She twice served for the match -- wasting a match point at 5-3 -- and both times dropped her serve. Trailing 3-1 in the tiebreaker, Li won the next five points. She converted her third match point when Errani sent a forehand into the net to improve to 6-0 in career meetings.
"The first match is always tight," said Li, who had a three-week break since her last tournament. "I still have to find the rhythm on the court."
Jankovic is ranked No. 8 and seeded seventh because third-ranked Maria Sharapova pulled out of the event with a shoulder injury. She proved to be the steadier player against Azarenka, the Australian Open champion.
In the first set, Jankovic needed 10 minutes to hold serve for a 5-3 lead. Azarenka saved two set points in the next game but sent a forehand wide on Jankovic's fourth in the 10th game.
Azarenka dropped her serve in the third game of the second set and held in the fifth despite serving three double-faults and facing four break points. But she could not trouble Jankovic on her serve and another forehand by Azarenka sailed long and gave Jankovic the match.
After losing the U.S. Open final to Serena Williams, Azarenka lost her opening matches in both Tokyo and Beijing before beating Errani on Tuesday.
The top two finishers in each group advance to the semifinals.