The 2004 gold medallist was game point down in the first game of what was effectively a shootout for a place in the last 16 at Wembley Arena but came through 22-20 21-11.
Abian spurned his chance to take the opener when, after making a brilliant diving recovery, he smashed a potential winner into the net.
The Indonesian made him pay for the miss and established a grip he did not relinquish to claim the qualifying spot from Group O.
Hidayat blamed the early start for his sluggishness in the opening stages.
I never play early mornings. It's too early for me, I'm not an early morning person.
Taufik Hidayat
He said: 'I never play early mornings. It's too early for me, I'm not an early morning person. My body is still adjusting. Because I play too early, it's like I'm still sleeping.'
India's Kashyap Parupalli sprang a surprise to go through at the expense of 10th seed Tien Minh Nguyen of Vietnam.
The world number 21 produced one of the best performances of his career to win 21-9 21-14 and top Group D.
Danes Kamilla Rytter Juhl and Christinna Pedersen stunned second seeds Tian Qing and Zhao Yunlei to secure one of the top two spots in Group D of the women's Doubles.
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