Dawson, who claimed the second title of his career earlier this year at a Champions Tour event in Tucson, after a previous minor win in 2002, added the greater prize of the senior major after a closing 64 saw off Montgomerie and last year’s champion Bernhard Langer.
Montgomerie, among those who had to complete their third rounds on Sunday morning, looked well placed to strike for victory at one stage when he led by himself on 14 under par, but back-to-back bogeys at 11 and 12 reined in his progress.
The 52-year-old Scot signed off with a three-under 67 for an aggregate 13-under 267, but that left him in third place, three adrift of the new champion.
German Langer matched Dawson’s 64, and like the American he finished with a birdie at the 18th. Dawson needed his three at the last as he finished just one ahead of Langer over 72 holes, with a 16-under aggregate.
The goatee-bearded Dawson, who split his earlier career between the PGA Tour and second-tier Web.com Tour, has seen his earnings soar since turning 50, the age at which golfers can migrate to the senior ranks.
Now aged 51, he began the final round in a share of first place on 10 under with Montgomerie, who has won three senior majors in the United States, and held his nerve as his celebrated playing partners looked to wrestle the lead away from him over the closing holes.
Dawson has never played the Open Championship before, but he will have that opportunity next year, with one perk of his Senior Open success being an exemption for Royal Troon next July.
Dawson said on Sky Sports: “Bernhard made a phenomenal par on the 16th and Colin made a phenomenal par at the 17th, and I thought ‘Wow, these guys aren’t going away, it’s going to be a little harder than I thought’.
“It was great to play with them to see how they play and how they react, and I thought, ‘They’re not doing anything different than I am. They’re hitting the same shots, making the same swings, making the same mistakes and making the same putts’, so I just made a few more putts.”