The 51 year old, whose best finish in 413 events on the US PGA Tour was runner up in the 1995 Greater Milwaukee Open, sank a dramatic and decisive 18ft birdie putt on the last hole for a round of 64 to finish one shot clear of defending champion Langer, who also closed with a 64, while Montgomerie was a further two shots back.
Langer, therefore, narrowly missed out on a record-equalling third Senior Open title, following his dominant 13 shot victory at Royal Porthcawl last year, but for Dawson it was an emotional maiden Senior Major Championship, after only capturing his first title on the US Champions Tour in March.
"This is unbelievable," said Dawson, who finished 16 under par for the Championship. "I can't tell you how many hours I put in on the range, and I've had two back surgeries to prove it. I've spent a lot of time on the range and on the putting green over the years, and you know, it's a little later than most of the guys, but it came true.
"I had a lot of fun last year. I wasn't expecting a lot but things started to happen and I started getting more and more confident. And then I won earlier this year, which gave me a lot of confidence through the rest of the season, and when I got to this point two days ago, and I had a good first round and a good second, I thought, okay, maybe this is going to happen again. I said we'll just keep on making the swings and try and make the putts. That's what it comes down to. I just made one more putt than Bernhard."
Dawson's victory also means he qualifies for next year's Open Championship at Royal Troon, which will be his first appearance in golf's oldest Major.
"Isn't that nice?" he said "So I'll be here two weeks next year. Great. I love that. I love the way the game is played over here. I love that you can play it on the ground, in the air. There's so many options, so many more options than we have in the States.
"Most of the play over there is in the air. Unfortunately it was wet this week. The first two days were very bouncy and you see a lot of balls run a lot. It's a lot of fun playing golf like that."
Langer continued his remarkable record in the Senior Open, finishing runner up for the second time after losing a play-off to Mark Wiebe in 2013, having finished no worse than 12th in eight appearances.
"It was an exciting week," said the two-time Masters Champion. "It's very befitting of the venue and the tournament. We had a great leaderboard, lots of good players up there, and a few lead changes as the day went by.
Peter Fowler finished as the leading Australian in 9th position with Peter Senior 12th.
Leading final round scores (par 70)
264 M Dawson (USA) 65 67 68 64,
265 B Langer (Ger) 65 68 68 64,
267 C Montgomerie (Sco) 67 67 66 67,
269 M JimÃƒÂ©nez (Esp) 65 69 68 67,
272 F Couples (USA) 68 66 69 69, W Austin (USA) 69 67 70 66,
273 J Maggert (USA) 71 67 66 69, P Walton (Irl) 71 67 65 70,
274 E Toledo (Mex) 73 68 68 65, J Sluman (USA) 65 69 70 70, P Fowler (Aus) 69 65 68 72,
275 B Bryant (USA) 65 70 70 70, B Lane (Eng) 68 70 68 69, P Senior (Aus) 69 67 70 69,
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