Stenson eagled the par-three fourth in a five-under outward nine and birdied the last after eight consecutive pars coming home.
The 2015 Scottish Open winner Rickie Fowler recorded a third successive 67 to trail by one shot.
Overnight leader Charley Hoffman followed up a second round 63 with a five-over 76 to tie 11th place.
In-form Stenson followed up his runner-up finish in The Barclays last week by posting a bogey-free third round and wipe out a five-shot deficit on the leader at the halfway stage.
The 39-year-old won in Boston two years ago, and then dominated at the Tour Championship to capture the FedEx Cup and the $10m (£6,590,000) bonus.
Scotland's Russell Knox is the best placed of the British contingent with a steady 68 to stand three off the lead at 10 under.
Ian Poulter is five under after hitting a 69, while fellow Englishman Luke Donald is three under after struggling to a 72.
Rory McIlroy who replaced Jordan Spieth as world number one last week, is off the pace in 64th after a level par round.