Harrington made a par at the first extra hole after both players finished regulation with scores of 5-under-par 283, four strokes ahead of the field.
Harrington, who led after Saturday's third round, managed a 1-under 71 Sunday, while Dredge, from Wales, equaled the course record with a 4-under 68.
Weather conditions were far less windy than they had been the first three days.
"I feel sorry for Bradley because he really came at me," the Dublin native said. "I felt the pressure. It was probably the most nervous I've been for many a tournament. I've always said that after the four Majors this is the next event I've wanted to win."