Starting with a two-shot lead on Sunday, Thompson made a 45-foot birdie putt on the opening hole and no one got any closer to him the rest of the way.
The 25-year-old American opened with five birdies in six holes, stretched his lead to six shots and ended up winning by four strokes from C.T. Pan (64), Michael Thorbjornsen (63) and impressive amateur Luke Clanton (63).
Thompson finished at 28-under 256 to break by one the John Deere Classic record set by Michael Kim in 2018.
Australia's Jason Day fired a closing 66 to finish tied 23rd, 12 shots behind the winner.
The victory gets Thompson into the next three majors, starting with the British Open in two weeks at Royal Troon. He also will make his Masters debut next April.
Thompson is the 24th player to get his first PGA Tour win at the John Deere Classic, the most of any tournament dating to 1970.
The final hour was all about who would finish second and earn the other spot to the British Open. That went to C.T. Pan of Taiwan, who birdied the 16th and 17th holes and finished with a two-putt par from 20 feet for a 64.
But a pair of American youngsters made him sweat it out.
Florida State sophomore Clanton holed a 25-foot birdie putt on the 18th hole for a 63 and was the first to get to 24 under.
Michael Thorbjornsen, the No. 1 player in the PGA Tour University ranking after finishing at Stanford, hit out of a fairway bunker to 18 feet and made the birdie putt for a 63 to join Clanton.
With a three-way tie for second, the British Open spot went to Pan based on the world ranking.
Clanton, meanwhile, became the first amateur since Billy Joe Patton in 1958 to finish in the top 10 in consecutive PGA Tour-sanctioned tournaments.
Patton was low amateur at the Masters and the US Open that year. Clanton tied for 10th at the Rocket Mortgage Classic last week.
Clanton's last two weeks would have been worth just over $US804,000 ($A1,192,000) had been pro.
Several players from Georgia have been renting a house near the John Deere Classic for the last few years. J.T. Poston stayed there when he won the Deere two years ago. Sepp Straka stayed in the house last year and won.
Straka brought his wife and young son with him this year and gave up his room to Thompson.
"I think I have to pay for the whole house, which is unfortunate," Thompson said with a smile. "But I'll gladly pay it."
The victory was worth $US1,440,000. It also moves Thompson to No.22 in the FedEx Cup standings, all but assuring he will be in all the signature events next year.
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