The defending champion was 8-5 down and, despite trailing in the penultimate frame, went on to win his 21st consecutive match in the event.
"When it went 8-8 I knew I'd gone in the head. I'm absolutely gutted," Hamilton said.
In the 16th frame, he had constructed a 68 break but, requiring only one more red to leave Hendry needing snookers, Hamilton surrendered position. He missed a red, and Hendry cleared to pink with 62 only to jaw the black off its spot.
The six-time world champion bowed his head, expecting the telling blow to be struck by Hamilton but he twice missed the black, the second time an elementary pot to a middle pocket - and Hendry was reprieved.
"I just kept battling away," Hendry said. "I'm cueing beautifully, but my concentration is terrible. If the pressure hadn't got to Anthony like it did, there's no doubt I would be on my way home by now."