Seeded 12th, the jet-lagged Serb who had reached the semi-finals in her last two tournaments struggled to find a rhythm as she was broken three times in the opening set and twice in the second.
World number one Victoria Azarenka had to work hard to extend her unbeaten record to 18-0 this year, beating Germany’s Mona Barthel 6-4 6-7 7-6, while 13th-seeded Russian Anastasia Pavlyuchenkova was ousted 6-4 6-4 by American Vania King.
Wimbledon champion Petra Kvitova, however, eased into the third round of the elite event with a 6-1 6-3 demolition of fellow Czech Barbora Zahlavova Strycova at Indian Wells Tennis Garden.
Hampton, who made her debut in the top 100 of the rankings last week, sealed her surprise victory in just under 90 minutes when a Jankovic forehand sailed wide on the stadium court.
“It was a bad day of tennis for me,” Jankovic, champion here in 2010, told reporters. “I just did not feel the ball. My legs felt so heavy on the court, so I was moving very badly out there.
“Hampton played solid. She was playing very well. I was really a shadow of myself. I guess it’s one of those days where you just come on the court and the legs don’t go, the reactions are not there.”
Jankovic had reached the last four in Dubai and Kuala Lumpur in her previous two events but felt her journey from Malaysia to the United States earlier this week had taken its toll.
“I was in good form in Dubai and Kuala Lumpur, but maybe just had not much time to get over (to the US), get over the jet lag and feel fresh before this tournament,” the former world number one said.
“Maybe that’s something maybe to do with it, but obviously there’s no excuse. I had to go out and perform much better than I did today, but it didn’t happen for me.”
Playing against the 99th-ranked Hampton for the first time, Jankovic was broken in the second, sixth and 10th games of the match to lose the opening set in 42 minutes.
Hampton, who upset 38th-ranked Polona Hercog of Slovenia in the opening round at Indian Wells, surged into a 5-1 lead in the second set before fending off a late Jankovic fightback.
The Serb broke the American in the seventh game, held serve in the eighth and then saved two match points in the ninth before her final forehand error.
“I was pretty nervous before the match,’ said Hampton, who lost in the first round on her Indian Wells debut last year. “I didn’t really know what to expect. I think the fact that I got a match under my belt here, the round before, helped me a lot.”
Top-seeded Azarenka, who won her first grand slam crown at the Australian Open in January, squandered a 5-1 lead in the second set and then came from 1-4 and 3-5 down in the third before sealing a tight victory 8-6 in the tiebreak.
“I won this match mentally more than physically or tactically or whatever,” the 22-year-old Belarusian said. “That was really what brought me a win today, my fighting spirit, till the last moment.”
In other second round matches, fifth seed Agnieszka Radwanska of Poland brushed aside Romania’s Sorana Cirstea while China’s eighth seed Li Na battled past Kazakhstan’s Galina Voskoboeva 3-6 6-3 6-3.
Slovakia’s 19th seed Daniela Hantuchova, Indian Wells champion in 2002 and 2007, was beaten 6-3 6-7 6-3 by Czech Klara Zakopalova. (Reporting by Mark Lamport-Stokes; Editing by Frank Pingue and Patrick Johnston)