In 1985, Baker won the Brabazon Trophy (tie with Roger Roper). He represented Great Britain & Ireland in the 1985 Walker Cup and turned professional the following year.
Baker was a consistent performer on the European Tour from the late 1980s until the early years of the new Millennium, with three tournament wins on the tour and a highest Order of Merit finish of seventh in 1993. His one Ryder Cup appearance for Europe came in the losing 1993 team, but he picked up three points out of four, beating Corey Pavin in the singles.
In 2007 Baker won two events on the second-tier Challenge Tour, the Credit Suisse Challenge and the Open AGF-Allianz Cí´tes d’Armor Bretagne on his 40th birthday. He also won the Mauritius Open at the end of 2007, beating José-Filipe Lima by three shots.
In 2009 Baker won once again the Credit Suisse Challenge.
Baker was one of Ian Woosnam’s vice-captains at the 2006 Ryder Cup.