Webster, who has struggled with a back injury this year, birdied the first three holes and then added five others with only one bogey. He leads former champion Paul Lawrie, Soren Hansen, Scott Strange and Hennie Otto by one stroke.
Many of the biggest names in the tournament also played at Carnoustie, including Ernie Els, Luke Donald and Niclas Fasth, who were among a group of 10 who shot 67.
Defending champion Padraig Harrington, the British Open champion at Carnoustie in July, shot 70, and Justin Rose had a 68.
The Old Course at St. Andrews and Kingsbarns are the other layouts used for the championship, but Webster benefited from the calm day at Carnoustie.
'It's always best to play this course when it's calm. The greens were perfect so you had to take advantage,' the Englishman said.
After his quick start, Webster made four more birdies on the last seven holes.
A group of 14 players at 68 included 2006 NCAA champion Jonathan Moore, a member of the victorious U.S. Walker Cup team in Ireland last month before turning professional.
The former Oklahoma State student played on the Old Course, which he had never seen until this week.
'It was a lot of fun,' Moore said. 'I made a lot of birdies, six, and I had a good chance at the last, too.'