Gotterup - caddied by his brother Patrick - was pushed to the limit by Ben Kohles, who shared the co-lead going to the 18th before finding the water with his second shot, eventually leading to a double-bogey that consigned him to a share of third place with Lucas Glover and Lee Hodges.
Runner-up Max Homa got himself back into contention with five birdies on the back nine, but his efforts were in vain as he finished 19 under - one shot off the eventual winning score.
- Leaderboard: John Deere Classic
- When are the majors? Key dates, results and 2026 schedule
- Not got Sky? Get Sky Sports or stream golf with no contract
"Just a special week," an emotional Gotterup said on Sky Sports.
"Even if we didn't play great it was going to be fine. [My brother] kind of got me to this point. To have a resurgence today was a lot of fun - you can't have a better day than today.
"I'll take a Sunday 62 any time I can - I'll pay a lot of money for them too!
"I feel like I've built a relationship with this tournament - having them give me a spot four years ago changed my life. To come back and win is so cool.
"My brain is moving at a million miles an hour - but just so fun today."
Ryo Hisatsune finished tied-ninth at 16 under after a final-round 67, while Keegan Bradley surged 29 places up the leaderboard with a 64 to finish tied-26th on 12 under.
The British contingent was led by Matt Wallace and David Skinns, who both finished outside the top 20 on 11 under, with Wallace notching an impressive final-round 65 to rise 22 places to a share of 33rd.
Watch the PGA Tour live on Sky Sports, with the ISCO Championship from July 9-12 live on Sky Sports. Get Sky Sports or stream with no contract.
