Despite his steady career, with wins on four continents, including Asia, Baker-Finch was not generally counted as a member of the elite group of international golfers. When he won the 1991 Open Championship at Royal Birkdale, closing with a 64-66 to beat Mike Harwood by two strokes, he was considered a surprise champion. He had three other runner-up finishes that year as well and again qualified for the Tour Championship with a 13th-place finish on the money list. He ranked briefly in the top-10 of the Official World Golf Ranking that year.