Allen reached the top of the world rankings for the first time in his career after the World Championship in May, before he was replaced by Judd Trump at the end of August.
Now third in the world, the 38-year-old has reached two semi-finals in 2024-25, losing to Mark Selby at the British Open in September and against Xiao Guodong in the Champion of Champions earlier this month.
Welshman Page led 3-2 but Allen, an 11-time ranking event winner, made his experience count as he won four of the next five frames to clinch victory.
However, Allen, who plays either China's Si Jiahui or Wu Yize in the last 16, was left bemused by his lack of form.
"I'm doing all the things that got me to world number one, working really hard on the practice table but it's not coming easy," he added. "I'm hoping one performance turns it around but I feel a million miles away from that.
"Jackson is a brilliant talent but not very experienced on the big stage so I thought I would take advantage of that and it nearly backfired.
"It's not fun, I'm not going to lie - I couldn't enjoy any part of that match. It's unsettling given how much I practice, and considering how hard I've been working. I'm probably not as far as I think I am, I'm my worst critic."