Baker-Finch turned professional in 1979. Baker-Finch credits Jack Nicklaus as his greatest influence, saying that he based his game on NIcklaus's book, Golf My Way. He began his professional career on the PGA Tour of Australasia, winning his first professional tournament, the New Zealand Open, in 1983. From 1984 to 1987 he was a member of the more prestigious PGA European Tour, and enjoyed moderate success on that tour, winning the 1985 Scandanavian Enterprise Open and finishing in the top twenty on the order of merit in both 1985 and 1986. At the same time he continued to play in Australasia in the Northern Hemisphere winter, picking up several further tournament titles there, and occasionally played on the Japan Golf Tour.
Baker-Finch first played on the PGA Tour as an invitee in 1985, and began to do so regularly in 1989, having qualified for tour membership by finishing third in the 1988 World Series of Golf. He won his first PGA Tour title at the 1989 Southwestern Bell Colonial, giving him a two-year exemption on Tour. In 1990, he finished 16th on the PGA Tour money list, on the strength of 3 runner-up finishes and 2 third-places.
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, and when he won his major championship at the 1991 British Open, 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.
Baker-Finch's British Open victory might have proved the catalyst for him to move to a higher level and start to regularly challenge for prestigious titles, but this was not to be the case. He had a 10-year exemption from the PGA Tour from the British Open win, leaving him exempt until 2001. He did achieve a runner-up finish in the Players Championship in 1992, but never came close to contending on the PGA Tour again. He picked up one relatively minor win outside the U.S in each of 1992 and 1993, but his form then went into a steep and accelerating decline. He started to lose confidence in his game, and tinkered with his swing often. His last top-10 finish on the PGA Tour was a tie for 10th in the 1994 Masters Tournament.
Baker-Finch then suffered a famously difficult-to-watch complete collapse of his game. The problems were often psychological: He would hit shots flawlessly on the practice range, and then go to the first tee and hit a weak drive into the wrong fairway. In 1995 and 1996 he missed the cut, withdrew after one round, or was disqualified in all twenty nine PGA Tour events that he entered. After shooting a 92 in the first round of the 1997 British Open, an extraordinarily bad score by tournament professional standards, he withdrew from the championship and retired from tournament golf.
Baker-Finch was hired by ABC Sports to commentate on golf tournaments in 1998, and still does that to this day. On broadcasts he is often known by the nickname "Finchy". The only PGA Tour event he has played since the 1997 Open Championship was the 2001 MasterCard Colonial, where he missed the cut with rounds of 74 and 77.