Ivanovic was leading 7-5, 1-0 when Hantuchova withdrew after falling 0-40 behind in the second game.
The match started slowly for Ivanovic, who surrendered her first two serves as Hantuchova took a 5-3 lead. But Ivanovic won the next four games to secure the set, winning the ninth game at love with her final three serves being aces.
"She started really well, and I managed to get back into the set and break her back," Ivanovic said. "I played some really good tennis towards the end of that first set and then in the second."
Wildcard entrant Alisa Kleybanova of Russia also advanced after her opponent retired.
At 5-5 in the first set, 10th-seeded Dominika Cibulkova of Slovak Republic, the recent Australian Open finalist, retired from the match with a gastrointestinal illness.
"I was really looking forward to playing this week in Doha," said Cibulkova, who was making her first tournament appearance since becoming the first Slovakian to reach a Grand Slam final.
"Unfortunately I became very sick today and suddenly did not feel well. I wanted to give it a try today and I did everything I could to try to play, but I could not continue."
Karin Knapp, who led Italy to a 3-1 Fed Cup victory over the United States in Cleveland at the weekend, was told she had to be in Doha to play a first round match on Tuesday.
Knapp started her journey early Monday morning and after going from Cleveland to Washington DC, and then to Dubai, she landed in Doha on Tuesday in time to play her afternoon match.
Knapp played impressive tennis to defeat Caroline Garcia of France 6-4, 6-1 straight off the plane.
Four players who chose to skip playing the Fed Cup tie between the U.S. and Italy in order to get to Doha early -- Sloane Stephens, Francesca Schiavone, Roberta Vinci and Flavia Pennetta -- have all lost their first round matches.
Elsewhere, American Bethanie Mattek-Sands upset 15th-seeded Eugenie Bouchard of Canada, a recent Australian Open semifinalist, 7-5, 6-1.