The 46-year-old Gillis, who was attempting to become the oldest first-time winner on the PGA Tour in 20 years, sent an approach into the water. Spieth made par for his second win at TPC Deere Run in three years and improved to 3-2 in playoffs in his career.
Now Spieth heads to The Open in search of his third consecutive major championship. He is the first golfer to win four times before The Open since Tiger Woods in 2000.
Jordan Spieth will try to become the 12th player to win a PGA Tour event the week before winning a major. Michael Cohen/Getty Images
Gillis' consolation is a bid into The Open. It will be his first major appearance since the 2011 PGA Championship.
After shooting a career-best 10 under Saturday, Spieth entered the final round with a two-shot lead. But the field caught up to him when he turned in a pedestrian front nine.
Spieth bogeyed two of his first three holes and was soon passed by the likes of Gillis and Johnson. Spieth was even at the turn and two shots back of Gillis, who in 171 previous PGA Tour starts had finished in the top three twice.
But Gillis played his final six holes at even par. Spieth roared back into contention with four birdies in five holes, including a 21-foot chip from the fringe on No. 16.
Spieth had a 30-foot putt for the win on No. 18, but he pushed it left. He nearly won on the first hole of the playoff, but his 33-foot try lipped out.
Gillis matched Spieth with a par on the first hole in sudden death. But a tee shot that went into the rough led to a shot in the water, effectively ending his bid for an elusive victory.
Gillis shot a 7-under 64 in the final round.
Lee, who was attempting to become the first player in 18 years to get his first two career victories in back-to-back events, bogeyed No. 18 when par would have earned him a playoff spot.
Johnson's round was delayed when, while standing over a possible birdie putt on No. 16, a loud booming sound that apparently came from a boat on the nearby Rock River startled him. He missed the subsequent putt.
The fifth PGA Tour win of Spieth's career comes two weeks before his 22nd birthday. Only Woods (6) has more tour wins before turning 22 since 1940.
The Associated Press and ESPN Stats & Information contributed to this report.