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.
He will face Robert Milkins (47) or Thepchaiya Un-Nooh (38), who square off later on Tuesday evening.
"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."
In Tuesday afternoon's other first-round match, John Higgins (48) saw off Joe O'Connor (28) by a score of 6-3.
Higgins from Scotland never trailed in the match and will face Neil Robertson (41) or Zhou Yuelong (25) in the next round.