Williams won the Champion of Champions title in November, two months after reaching the final of the Saudi Arabia Masters, and is ranked sixth in the world.
He required all of his years of experience to get over the winning line against Chinese qualifier Wu, who produced some stunning scoring in the first session and pushed Williams hard before the left-hander eventually wrapped up a 10-8 victory.
“It’s good for me [to be tested] because I finished off really strongly,” said Williams, who will play Iran’s Hossein Vafaei in round two. “I potted a couple of long ones and made a frame-winning break in the last frame.
“It’s in the tank, it’s been in the tank all season. I’ve won a tournament, I got to the final of another big one and lost a few first-rounders.
“You just want to win in the first round here because if you lose on the Saturday or Sunday, you don’t really feel like you’ve been in the tournament because it doesn’t really start until the second week.
“I’m over the moon to get through, I could easily have been out and watching the rest on television, but I’ll go home, come back up on Wednesday or Thursday and go again.”