Taking up where he left off when getting in the mix on the last day in the Open Championship at Carnoustie, Woods opened his bid for a ninth triumph in the WGC-Bridgestone Invitational with a four-under-par 66 at Firestone Country Club in Akron.
Starting at the tenth, the 42-year-old birdied the 11th, 16th and 18th going out then made further gains at the fifth and seventh before dropping his only shot of the day at the ninth, his last.
As American Kyle Stanley set the clubhouse target with a seven-under 63, McIlroy carded a bogey-free 65 while Knox had five birdies in a 67.
Meanwhile, Montgomerie carded a course-record eight-under-par 63 – his lowest-ever round on the Staysure Tour – at London Golf Club to take a one-shot lead in the Staysure PGA Seniors Championship.
“It was a very good round – no bogeys, nine birdies,” said the big Scot. “I always enjoy playing with Paul McGinley and I usually play quite well with him. There was a good rhythm and we played well together.”
Montgomerie’s compatriot, Gary Orr, is lying joint-fifth after a 66, with Andrew Oldcorn a shot further back.
Still in the paid ranks, Liam Johnston and Jack McDonald made the best start among the Scots in the Swedish Challenge with matching four-under 68s in an event being hosted by Robert Karlsson. On his pro debut, Open Championship Silver Medal winner Sam Locke carded a level-par 72.
Elsewhere, brothers Sandy and Calum Scott from Nairn both progressed to the last 16 in the Scottish Amateur Championship at Blairgowrie.
Others still standing at the Perthshire venue after the opening two rounds include top qualifier Callum Bruce (Duff House Royal) and 2016 Scottish Order of Merit winner Euan McIntosh.