Johnson shot a bogey-free, five-under-par 65, driving a lot of three-irons off the tees into the fairways and hitting 16 of 18 greens in regulation.
"I've got to keep doing what I'm doing," Johnson said. "I've got a pretty good game plan for the golf course off the tee. So I'm going to stick to that, just trying to keep getting birdie looks on every hole."
His only birdie on the back nine was a two-footer at the 177-yard 16th hole. That was enough to lead after his front-side 31, which included a 45-foot birdie putt on the difficult par-four fifth hole.
Jimmy Walker, a three-time winner this season, and 20-year-old Dallas native Jordan Spieth were in a group of 10 players at 67.
Scott had bogey on the straight par-five, 631-yard 11th hole, his second of the day, when he hit twice from fairway bunkers. After a two-putt from 11 feet at the 433-yard 18th hole, Scott was bogey-free the rest of the way, with consecutive short birdies after making the turn.
Johnson's 65 was the highest score to lead after the first round at Hogan's Alley since another 65 in 2002. There were opening 62s in two of the previous three Colonials.
Catriona Matthew took the first-round lead in the Airbus
The 44-year-old Scot rebounded from a bogey on the par-four 12th — her third hole in the morning round — with the eagle on the par-5 13th and birdied seven of her final 11 holes.
Charley Hull had a bogey-free 65 in the afternoon. The 18-year-old English player birdied the final two holes on the Crossings Course at the Robert Trent Jones Golf Trail's Magnolia Grove complex.
Second-ranked Stacy Lewis, No. 4 Suzann Pettersen and South Korea's Eun-Hee Ji shot 66. Lewis, the 2012 winner, finished her first nine with birdies on Nos. 15-18.
However, poor weather forced two separate delays totaling nearly two hours in the European Tour's flagship event, and darkness halted play with 33 in the 150-man field yet to complete their first round.
It is the third occasion in Bjorn's 21-year European Tour career he's shot a round of 62.
Rafa Cabrera-Bello of Spain was alone in third place with a 65, and Gary Stal of France made the most of his last minute call-up by shooting a 66. Stal was first reserve for the event, and took the place of countryman Victor Dubuisson, who pulled out injured.