In the first set, Hingis dumped an easy volley into the net to lose a game, then smacked the net cord with her racket in anger. The crowd on Court 1 hooted and whistled as she walked to her chair.
That was Hingis' only fit of anger, and the crowd politely applauded her the rest of the way. Last year fans booed when she blew a lead and threw a tantrum in the final against Steffi Graf.
"People so far have been very nice to me,'' Hingis said. "It was a good match, long rallies, good points. For sure I hope it made them happy. That's what we're there for. We're kind of the entertainers.''
The top-seeded Hingis struggled against Abe, a 24-year-old German ranked 156th. Abe came into the tournament with five consecutive losses, but she took a 2-0 lead in each set, and her powerful forehand kept Hingis scrambling.
"That girl played very well,'' Hingis said. "I know that she can play some really good tennis.''
Hingis won four games in a row for a 5-3 lead in the first set, then blew the putaway volley that prompted her to take a swipe at the net cord, making the score 5-4. She shook off the brief jeers in the next game, breaking serve to win the set.
In the second set fans applauded both players, although they clearly favored the underdog. Abe, pumping her fist to celebrate big shots, had Hingis panting and leaning on her racket after one long rally.
Abe won a 16-point game for a 5-4 lead in the second set, but Hingis then took charge, winning 12 of the final 15 points. A perfect forehand lob put Hingis ahead 6-5, and Abe folded with three consecutive unforced errors in the final game.
Hingis, 19, is seeking the only Grand Slam title she hasn't won.
"I think this is the most difficult one,'' she said. "I just take it day by day. That's all I can do right now.''