White, a former Masters and UK Championship winner, hit five half-centuries to earn a slice of history at the Tempodrom.
It made him the first player aged 60 or older to reach the last 16 of a ranking event since Eddie Charlton achieved the same in 1992 at the British Open.
Six-time World Championship runner-up White started with a 55 break and despite Peng being able to level immediately after, the Chinese made a costly error in the third frame when his rest knocked the pink.
White claimed the close third frame and did not look back with breaks of 82, 63, 50 and 70 sending the veteran through to face Jack Lisowski next.
"Just really enjoying playing and I just want to compete," the 60-year-old told World Snooker Tour.
"I am fighting to stay on the tour, on the one-year list I am on, but I need to go deep in either this tournament or the Welsh or the new tournament they will put in. So, if I can get to Sheffield knowing I have secured my place it would take a lot of pressure off me."
Lisowski, a runner-up in Berlin two years ago, beat Zhang Anda 5-0 with an impressive 117-break along the way.
Tian Pengfei eased past Anthony McGill 5-1 and will take on Tom Ford next.
Ford received a walkover having been drawn against defending champion Zhao Xintong, one of four players who were set to be involved in the tournament that are currently suspended due to ongoing match-fixing claims.
World number eight Kyren Wilson safely negotiated his way past Sam Craigie 5-2.
Elliot Slessor beat Joe O'Connor 5-2 and will next take on Xiao Guodong, who edged out Fan Zhengyi in a deciding frame.