Noren was looking to win a second title in Scotland in the space of a month, after capturing the Scottish Open on July 10, and was 2 up after two holes over the Archerfield links in the windiest conditions of the week.
He didn't win another hole.
Wall, ranked No. 234, won Nos. 3, 6 and 11, and saw Noren miss a birdie putt from 12 feet at the par-5 last that would have taken the match to extra holes.
Wall's only previous title was at the Alfred Dunhill Championship in 2000 - 16 years, 204 days ago. He has played 431 events since then, and has struggled over the past three years with hip and back injuries.
''I thought my time had passed, I have to be honest,'' Wall said.
The 41-year-old Wall played 107 holes in six matches in eastern Scotland.
''I've been struggling all year, not feeling well,'' he said. ''And then this week, I've been really enjoying myself.''
In the third-place playoff, Oliver Fisher was a 4-and-2 winner over fellow Englishman James Morrison.