It was the first time Hingis has played the event since claiming the title in 2000 with victory over Lindsay Davenport, after twice finishing as runner-up.
Hingis is a contender for the eight-player field at the season-ending WTA Championship to be held in Madrid in two weeks. She is in eighth position, with the greatest threat to her place coming from fellow-Swiss Patty Schnyder.
Groenefeld played with her left leg tightly strapped above the knee and Hingis needed to do little but wait for the unforced errors.
The match became a contest in the second set, but Hingis always retained the advantage, holding a break point at 4-3 and two match points at 5-4, before Groenefeld sent a crosscourt forehand wide at 6-5.
Hingis, looking back on her comeback year with satisfaction, said: "If somebody had asked me if I was going to be in the top 10 at the end of the year I'd have thanked them with a hand kiss."
The Swiss added: "Just playing great matches against the top five players in general was a great achievement for me. I felt I still had it in me and I proved it."
In the only other match on the opening day of the tournament, Slovenia's Katarina Srebotnik earned a second round meeting with fourth-seeded Russian Elena Dementieva with a 6-3, 7-5 win over Mary Pierce of France.
French world number one Amelie Mauresmo, the top seed, has a first round bye before playing Australia's Samantha Stosur or a qualifier.
Russia's Maria Sharapova, who withdrew from her quarter-final in Moscow last week with a right foot injury and also has a bye, will face Israel's Shahar Peer or wild card Alicia Molik of Australia in the second round.
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