The German, who missed out on qualifying for the Ryder Cup team by just £36,000 but took up captain Nick Faldo's invitation to travel to Valhalla for the experience, was also playing the Old Course and went to the turn in 35.
A birdie at the 12th then took the 23-year-old to nine-under.
That chasing pack included Northern Ireland's Rory McIlroy, who was playing Carnoustie — the hardest of the courses — Denmark's Soren Hansen and David Howell.
McIlroy, third in this event last year in only his second tournament as a professional, is seeking his first European Tour title after narrowly missing out in last month's European Masters in Switzerland, losing to Jean-Francois Lucquin in a play-off.
Howell finished seventh on the order of merit in 2005 and third the following year, but slumped to 142nd last year after a season blighted by injuries and loss of form.
But the 33-year-old from Swindon has shown signs of recapturing his best form this season and finished 16th at The Belfry on Sunday.
Westwood, meanwhile, was four shots off the lead on five under par at the turn, one ahead of Harrington, who birdied five of his last six holes in an opening 67 at Kingsbarns yesterday but was one over par for his round today.
