O'Sullivan - a seven-time winner of the event - slipped to a 2-0 deficit early on but managed to reel off six in a row to move into the second round.
"I find the matches quite long and hard now," O'Sullivan told the BBC after progressing.
"The more I play, if I win two or three matches in a tournament, you get used to it, but I find it harder to concentrate and have the hunger.
"Against someone like Anthony, it's not about playing well, it's about digging deep and out battling them. That's hard at my stage."
O'Sullivan will next face Robert Milkins after the Englishman dramatically won three frames in a row to come from 5-3 down to beat Thailand's Thepchaiya Un-Nooh 6-5 in the evening session.
Earlier, John Higgins saw off Joe O'Connor by a score of 6-3.
The 48-year-old from Scotland never trailed in the match and will come up against Zhou Yuelong who stunned former champion Neil Robertson 6-2.
Robertson tied the match at 2-2 but could only watch as Zhou potted breaks of 136, 134 and 99 to win the next four frames and dump the Australian out of the tournament.
